These are consolidated appeals by Rochdale Village, Inc. (“Rochdale"), in two cases arising out of a labor dispute between Rochdale and Public Service Employees Union, Local No. 80, International Brotherhood of Teamsters, Chauffeurs, Warehousemen and Helpers of America (the “Union”). Following a demand by the Union in January 1979 for arbitration of the dispute, Rochdale commenced suit in the Eastern District of New York for a stay of arbitration. Chief Judge Mishler denied Rochdale’s motion for a preliminary injunction and granted the Union’s cross-motion to compel arbitration. Rochdale appealed. Prior to the date scheduled for argument of the appeal, the arbitrator rendered his award and this Court granted a motion to postpone argument pending proceedings relating to the award.
The arbitrator ruled in favor of the Union, which brought suit in the Eastern District to confirm and enforce the award. Judge Mishler directed Rochdale to comply with the award, and Rochdale’s appeal from that judgment was expedited and consolidated with its earlier appeal.
The fundamental dispute between the parties is whether Rochdale violated its collective bargaining agreement with the Union by subcontracting, commencing November 1, 1978, for certain services formerly provided by some of the Union’s members. A threshold question in this dispute is whether the collective bargaining agreement terminated on October 31, 1978. Rochdale argues that the district court itself should have decided whether the agreement terminated on October 31, rather than referring that question to the arbitrator. For reasons that will appear, we find that certain questions relating to termination were not arbitrable, and reverse in part and remand for their determination by the district court.1
I
Appellant Rochdale is a cooperative housing development in Queens, New York. The appellee Union represents 175 maintenance workers and 53 security workers employed by Rochdale who are currently on strike. Rochdale and the Union entered *1293into a collective bargaining agreement, dated November 1, 1976, which contained the following duration clause (Article XXIV):
This agreement shall continue in effect until the 31st day of October 1978, and 'thereafter shall be automatically renewed for successive yearly periods unless written notice is given, by either party to the other, of its desire to modify, amend or terminate this Agreement. Such notice shall be given not more than seventy-five (75) days nor less than thirty (30) days prior to the expiration date of this agreement or of any annual extension thereof.
In Article III, Section 4 of the agreement, Rochdale agreed that no work of the type covered by the agreement would be subcontracted in whole or in part to any person not covered by the agreement. Other sections of the agreement prohibited strikes and lock-outs.
Article XX, Section 2 of the agreement provided that “[a]ny and all disputes hereunder shall be subject to binding arbitration, upon the request of either party hereto.” There was no provision requiring that amendments or waivers of the agreement be in writing.
During the summer of 1978, the parties exchanged a series of letters concerning renegotiation of the agreement. The Union’s first letter, dated June 8, contained fifteen “proposals for new contract.” Its second letter, dated July 11, stated: “you are hereby notified that the collective bar-' gaining contract now in effect between the Company and the Union shall terminate, in accordance with its provisions, on 10/31/78.” Rochdale’s first response, dated July 18, 1978, stated that Rochdale had “tentatively decided to discontinue its guard and security operations effective October 31, 1978 and to contract performance of these services to an outside vendor.” There followed four more letters from Rochdale, dated August 7 through August 15, relating to Rochdale’s own proposals to modify the agreement, including a letter dated August 8 addressed to the Federal Mediation and Conciliation Service, a copy of which was sent to the Union, stating that, “the subject collective bargaining agreement is to expire on October 31,1978.”
Negotiations commenced on August 2 and continued intermittently through October. Throughout it appears that the Union sought a new contract covering both security guards and maintenance employees, while Rochdale sought only maintenance services, preferring to subcontract for security services. During the pendency of the negotiations Rochdale advised the Union by letter dated October 3, 1978 that it had finalized its “decision to subcontract security services effective November 1, 1978.” The parties apparently exchanged no correspondence between the letters dated August 15 and October 3.
The negotiations for a new contract were unsuccessful, and at midnight, October 31, 1978 Rochdale discharged its security guards, who were replaced by employees of a security service contractor, International Bureau for Protection and Investigation, Ltd. (IBPI). The Union thereupon called a strike of all of its members employed by Rochdale.
Two state court lawsuits were brought as a result of the strike. On November 1, Rochdale filed suit against the Union seeking to enjoin picket-line violence and to obtain other related relief pursuant to N.Y. Labor Law § 807 subd. 1(f) (McKinney 1977). The action was dismissed for failure to comply with that section’s pleading and procedural requirements.2 On November 22, IBPI brought an action seeking to enjoin the Union from interfering with the Rochdale-IBPI contract. This action also was dismissed, the court holding that IBPI had failed to meet the pleading and standing requirements of § 807, and had failed to state a cause of action.3 In these two pro*1294ceedings the Union repeatedly took the position that the contract had expired on October 31, 1978.
In January 1979, the Union demanded arbitration of the dispute pursuant to the arbitration clause of the collective bargaining agreement, contending for the first time that the agreement had not expired on October 31 but instead had been automatically renewed, and that Rochdale consequently had breached the agreement by subcontracting for security services.4
Rochdale thereafter brought the first of the present actions under § 301(a) of the Labor-Management Relations Act, 29 U.S.C. § 185(a) (1976), seeking to stay arbitration on the ground that the collective bargaining agreement had expired prior to the effective date of the subcontracting. It urged that the expiration question be decided by the court. The Union cross-moved to compel arbitration of all issues, including questions of termination. It contended that the exchange of letters in the summer of 1978 proposing modification of the collective bargaining agreement had not been within the time period provided by the duration clause of the agreement and therefore did not terminate the agreement on October 31. The Union argued that the disputes clause of the agreement was sufficiently broad to require arbitration of this termination question. The district court agreed and ordered arbitration of all issues.
The arbitrator ruled that, because neither party had served written notice of termination or proposed modification during the 75-to-30 day period provided in the agreement, the agreement had not been terminated on October 31 but had automatically been renewed for one year commencing November 1, 1978. Rochdale was directed to reinstate all striking employees, and to remove IBPI’s personnel from its premises. The district court subsequently confirmed this award, reiterating its view that “the contract termination question clearly involves the interpretation and application of a specific provision of the collective bargaining agreement ... to wit, Article XXIV, captioned ‘Duration of Agreement.’ . . [W]e have before us the agreement of the parties to arbitrate ‘any and all disputes.’ In our view, this arbitration clause encompasses a dispute over the termination of the contract.”
II
There is no general duty to submit labor disputes to arbitration. Rather, “arbitration is a matter of contract and a party cannot be required to submit to arbitration any dispute which he has not agreed so to submit.” United Steelworkers of America v. Warrior & Gulf Navigation Co., 363 U.S. 574, 582, 80 S.Ct. 1347, 1353, 4 L.Ed.2d 1409 (1960). Thus, whether or not a party is bound to arbitrate a given issue is a matter to be determined “on the basis of the contract entered into by the parties.” Atkinson v. Sinclair Refining Co., 370 U.S. 238, 241, 82 S.Ct. 1318, 1320, 8 L.Ed.2d 462 (1962).
The question whether the parties have entered into a contract imposing a duty to arbitrate is one that must be decided by the court, not by an arbitrator. Steelworkers v. Warrior & Gulf Navigation Co., supra. See National Marine Eng’rs Beneficial Ass’n v. Globe Seaways, Inc., 451 F.2d 1159 (2d Cir. 1971);5 Procter & Gamble Independent Union v. Procter & Gamble Mfg. Co., 312 F.2d 181 (2d Cir. 1962), cert. denied, 374 U.S. 830, 83 S.Ct. 1872, 10 L.Ed.2d 1053 (1963). In making its determination, however, a court must be ever mindful of the strong national policy favoring arbitration of labor disputes. See Labor-Management Relations Act §§ 201(a), *1295203(d), 29 U.S.C. §§ 171(a), 173(d). Arbitration clauses are to be construed broadly, and there is “a strong presumption favoring arbitrability.” Nolde Bros., Inc. v. Local No. 358, Bakery and Confectionery Workers Union, 430 U.S. 243, 254, 97 S.Ct. 1067, 51 L.Ed.2d 300 (1977). The application of this policy is clearest when a party asserts that a particular type of claim falls outside the scope of an arbitration clause. In such cases,
[a]n order to arbitrate the particular grievance should not be denied unless it may be said with positive assurance that the arbitration clause is not susceptible of an interpretation that covers the asserted dispute. Doubts should be resolved in favor of coverage.
Steelworkers v. Warrior & Gulf Navigation Co., supra, 363 U.S. at 582-83, 80 S.Ct. at 1353.
Because the duty to arbitrate can be imposed only by contract, it often occurs that questions of contract termination must be decided in order to determine whether a party is under such a duty.6 Generally such questions of contract termination are for the court rather than for the arbitrator. E. g., Procter & Gamble Independent Union v. Procter & Gamble Mfg. Co., supra; see Bressette v. International Talc Co., 527 F.2d 211, 215 (2d Cir. 1975). But termination is not invariably a non-arbitrable question, for arbitration clauses vary widely in their scope, and contracts may be terminated in any of a number of ways.
If a court finds that the parties have agreed to submit to arbitration disputes “of any nature or character,” or simply “any and all disputes,” all questions, including those regarding termination, will be properly consigned to the arbitrator: “With that finding the court will have exhausted its function, except to order the reluctant party to arbitration.” United Steelworkers of America v. American Manufacturing Co., 363 U.S. 564, 571, 80 S.Ct. 1363, 1364, 4 L.Ed.2d 1403 (1960) (Brennan, J., concurring). See International Union of Operating Eng’rs, Local 150 v. Flair Builders, Inc., 406 U.S. 487, 92 S.Ct. 1710, 32 L.Ed.2d 248 (1972); Auto, Marine & Specialty Painters Local 1176 v. Bay Area Sealers, Inc., 577 F.2d 609 (9th Cir. 1977). In dealing with a narrower arbitration clause, a court’s inquiry is not so circumscribed, and it will be proper to consider whether the conduct in issue is on its face within the purview of the clause. Procter & Gamble Independent Union v. Procter & Gamble Mfg. Co., supra; Chattanooga Mailers Union, Local No. 92 v. Chattanooga News-Free Press, 524 F.2d 1305 (6th Cir. 1975); International Union, United Automobile, Aerospace and Agricultural Implement Workers of America v. International Telephone & Telegraph Corp., Thermotech Division, 508 F.2d 1309 (8th Cir. 1975). For example, if an arbitration clause covers only employee grievances, the court should not compel arbitration of questions of contract termination. M. K. & O. Transit Lines, Inc. v. Division No. 892, Amalgamated Association of Street, Electric Railway and Motor Coach Employees of America, 319 F.2d 488, 491 (10th Cir.), cert. denied, 375 U.S. 944, 84 S.Ct. 350, 11 L.Ed.2d 274 (1963).7 But if the arbitration clause covers disputes as to con*1296tract interpretation, and the termination is alleged to have occurred on a basis “implicit in [the] contract,” the termination question is arbitrable. Local Union No. 4, International Brotherhood of Electrical Workers v. Radio Thirteen-Eighty, Inc., 469 F.2d 610 (8th Cir. 1972).
Ill
The arbitration clause in the collective bargaining agreement between Rochdale and the Union is broad, but it is not unlimited. The agreement requires arbitration of “any and all disputes hereunder.” The insertion of the word “hereunder" after the otherwise all-inclusive phrase “any and all disputes” has the effect of limiting, albeit slightly, the parties’ duty to arbitrate. All disputes arising “under” the agreement are to be arbitrated; those that are collateral to the agreement are not.
The function of the court in dealing with this clause in the context of the present controversy is to ascertain whether any of the methods by which termination may have occurred was dependent on the construction or effect of terms of the contract. The record reveals several possibilities. First, the parties may have effected termination pursuant to the duration clause of the collective bargaining agreement. Second, the parties may have entered into a separate, side agreement that the collective bargaining agreement would definitely terminate on October 31. Finally, the Union may have repudiated any extension of the agreement beyond October 31. These possibilities raise separate issues of arbitrability.
A. Termination in accordance with the duration clause
The duration clause specified that the agreement would be renewed automatically unless either party gave notice of its intention to terminate or modify within a period 75-to-30 days prior to the expiration date of the agreement. Rochdale contends that August 17 was the 75th day prior to the expiration of the agreement; the Union asserts that August 18 was the 75th- day. Rochdale contends that its letter dated August 15 could not have been received by the Union until August 17 or 18, and thus was a notice within the 75-to-30 day period.
The questions as to when the notice period began, and whether the Rochdale letter constituted compliance with the duration provision are questions arising “under” the collective bargaining agreement. They depend on the construction or effect of the duration clause, and the dispute as to whether termination occurred in this manner falls within the scope of the arbitration clause. Thus, if termination did not occur by a means that was collateral to the agreement, this dispute was properly submitted to the arbitrator.
B. Termination by separate agreement
On the record before us it is entirely possible that the parties entered into a separate agreement that the collective bargaining contract would terminate as of October 31. The parties’ correspondence during the summer of 1978 indicates that both sides believed the agreement would terminate on October 31, each side stating precisely that the agreement would end on that date. Starting in August and continuing through October, the parties engaged in face-to-face negotiations over the terms of a new contract. In the state court litigation that followed the Union’s strike each party asserted that the agreement had been terminated on October 31.8 The earliest intimation that either party believed that the contract had not in fact terminated on October 31 came in January 1979, when, in the third month of the strike, the Union first demanded arbitration. On the facts now before us it is possible that the parties could be found to have agreed upon a definite termination date of October 31.
*1297If there was such an agreement it was collateral to the collective bargaining agreement. The latter agreement made no provision for alteration of the duration provision. The collective bargaining agreement was silent on the subject of any amendments to its terms; it contained nothing prohibiting or restricting amendment or requiring amendments to be in writing. Thus questions as to whether the parties entered into a side agreement or as to what the terms of such a side agreement were, do not arise “under” the collective bargaining agreement. This issue was therefore beyond the scope of the arbitration clause and should have been determined by the court. See International Union, United Automobile, Aerospace and Agricultural Implement Workers of America v. International Telephone & Telegraph Corp., Thermotech Division, supra.
Since the district court did not consider these issues, we are constrained to remand for further fact-finding and for a determination of whether the collective bargaining agreement was terminated by separate agreement of the parties.
C. Repudiation by the Union
It is also possible that the Union repudiated any extension of the collective bargaining agreement beyond the October 31 date. Repudiation, however, is nothing more than a unilateral attempt to terminate the agreement. If the contract allows a party to terminate unilaterally, a proper “repudiation” ends the contract and the parties’ contractual obligations; if the contract does not provide a right to terminate unilaterally, repudiation does not terminate the contract, but instead breaches it. See Restatement of Contracts §§ 317, 318. In either event, a claim that the effect of the repudiation was to terminate the contract necessarily requires an interpretation of the terms of the contract. While under principles of general contract law a material breach may discharge the non-breaching party of all contractual obligations, see Restatement of Contracts § 397, the strong presumption of arbitrability in the labor relations area prevents a breach-created discharge of the contractual duty to arbitrate disputes arising “under” the contract. See H & M Cake Box, Inc. v. Bakery & Confectionery Workers Union, Local No. 45, 493 F.2d 1226 (1st Cir.), cert. denied, 419 U.S. 839, 95 S.Ct. 68, 42 L.Ed.2d 66 (1974); General Dynamics Corporation v. Local 5, Industrial Union of Marine and Shipbuilding Workers of America, 469 F.2d 848, 853-54 (1st Cir. 1972). See also Controlled Sanitation Corporation v. District 128, International Association of Machinists and Aerospace Workers, 524 F.2d 1324 (3d Cir. 1975), cert. denied, 424 U.S. 915, 96 S.Ct. 1114, 47 L.Ed.2d 319 (1976).
Under Rochdale’s collective bargaining agreement as written, therefore, the question of repudiation was arbitrable and the district court properly declined to decide this question. Of course, actions by the Union arguably constituting repudiation may be highly relevant to the question of whether the parties mutually agreed, by words or conduct, to allow the collective bargaining agreement to lapse on October 31. As we have indicated above, the question of whether there was such a side agreement must be decided by the court. The issue of repudiation itself, however, if there was no collateral agreement, was for the arbitrator.
The order of the district court compelling arbitration is reversed insofar as it compelled arbitration with respect to issues not arising “under” the agreement. As to the remainder of that order and as to the judgment confirming the arbitrator’s award, the order and judgment are vacated and the cause is remanded for further proceedings consistent with this opinion. If the district court determines that the parties agreed to consider the agreement terminated, or that the Union is collaterally estopped from claiming renewal, judgment may be entered in favor of Rochdale in its action (No. 79-7200), and the Union’s action (No. 79-7440) should be dismissed. Otherwise, a new judgment may be entered nunc pro tunc ordering arbitration and a new judgment may be entered confirming the arbitrator’s award.
. We therefore do not reach the other questions raised in these appeals.
. Rochdale Village, Inc. v. Beverly, 96 Misc.2d 1080, 410 N.Y.S.2d 508 (Sup.Ct. Queens County 1978).
. International Bureau for Protection & Investigation, Ltd. v. Public Serv. Employees Union, Local 80, 98 Misc.2d 409, 413 N.Y.S.2d 962 (Sup.Ct.N.Y. County 1979).
. The Union also contended that Rochdale violated the ban on subcontracting by signing the contract with IBPI, the effective date of which was November 1, on September 29, while the collective bargaining agreement was still in effect. The arbitrator found that this did not constitute a violation.
. In Globe, this Court determined that the Association’s failure to comply with a condition precedent to effectiveness of the agreement — a condition imposed by the executory agreement itself — prevented the agreement, and thereby its arbitration clause, from coming into effect.
. In some circumstances the contractual obligation to arbitrate has been held to survive the termination of the agreement. See Nolde Bros., Inc. v. Local No. 358, Bakery & Confectionery Workers Union, 430 U.S. 243, 97 S.Ct. 1067, 51 L.Ed.2d 300 (1977), in which the Supreme Court held arbitrable a claim by the union that the contract gave employees a vested right to severance pay, even though the. claim was first raised when the employer discharged the employees after the contract had terminated. Nolde does not alter the importance of the termination question in the present case because the Union’s claim here is not analogous to that asserted in Nolde and because the Nolde arbitration clause extended to “any” grievance arising between the parties, id. at 245, 97 S.Ct. 1067, and was not limited to those arising “under” the agreement. See text at III infra.
. See also Trans World Airlines, Inc. v. Beaty, 402 F.Supp. 652 (S.D.N.Y.1975), aff'd without opinion, 94 LRRM 2125 (2d Cir. 1976); Oil, Chemical & Atomic Workers Int’l Union v. American Maize Prods. Co., 492 F.2d 409 (7th Cir.), cert. denied, 417 U.S. 969, 94 S.Ct. 3173, 41 L.Ed.2d 1140 (1974).
. Indeed, Rochdale asserts that as a result of the judgments in these two state court actions, see notes 2 and 3 supra, the Union is collaterally estopped from asserting that the agreement has been automatically renewed. This raises an issue for the court and should be considered on remand.