Chief Judge:
Glover Bottled Gas Corp. (the Company) appeals from an order of the United States *480District Court for the Eastern District of New York, Jack B. Weinstein, Ch. J., denying appellant’s application to stay arbitration and granting the application of Local Union No. 282, International Brotherhood of Teamsters, Chauffeurs, Warehousemen and Helpers of America (the Union), to compel arbitration. Glover claims that the dispute between the parties is not arbitra-ble. We conclude that it is, for reasons given below, and we affirm the judgment of the district court.
I.
From the scanty record before us, the following appear to be the pertinent facts: In May 1980, the Company and the Union entered into a collective bargaining agreement covering the drivers at the Company’s terminal in Patchogue, Long Island. By its terms, the contract was to continue until July 31, 1982; there was no automatic renewal clause. On July 19, 1982, the police investigated a theft of $1,947.81 in checks, and $439.25 in cash that had occurred on the Company’s premises on July 17. The police determined that the theft was an “inside job” and identified five employees as suspects. The five were asked to take lie detector (polygraph) tests; two agreed to do so and three refused. One of the three was the shop steward and another was the assistant shop steward under the labor agreement. The shop steward spoke to representatives of the Union and was advised not to take the tests because it was the Union’s policy to bargain about such a request by an employer. The three employees then told Company representatives that they would follow the Union’s advice.
On July 27, 1982, representatives of the Company and the Union had their first meeting to negotiate a new labor contract; the current one was due to expire in four days. At that bargaining session, one of the union representatives told the Company that the Union wanted “to bargain about Unit employees being requested to take polygraph tests,” but no agreement was reached. The next bargaining meeting was scheduled for August 10, 1982.
On July 28, the Company’s general counsel, who had also been at the bargaining session the day before, wrote to the three employees that the Company regarded their refusal to cooperate in the investigation of the theft by the police as “an extreme dereliction of duty, and an attempt to shield the guilty party,” and that failure to reconsider their refusal to take a polygraph test by August 4, 1982 would result in their discharge. A copy of one such letter, which was sent by certified mail, is reproduced in the margin.1 On August 4, 1982, the three employees were discharged.
*481There then followed in fairly short order the Union’s notice under New York law of intention to arbitrate, the Company’s petition in the New York State Courts for a stay of arbitration, the Union’s answer and counter-application to compel arbitration, and removal of the proceedings to the federal court. After the matter was argued before Judge Weinstein, he denied the Company’s petition and granted the Union’s. This appeal followed.
II.
As we have frequently noted, see, e.g., Conticommodity Services Inc. v. Philipp & Lion, 613 F.2d 1222, 1224 (2d Cir.1980), a district court’s scope of inquiry in considering a petition to compel arbitration under section 4 of the Federal Arbitration Act, 9 U.S.C. § 4, is circumscribed. The relevant statutory language provides:
A party aggrieved by the alleged failure, neglect, or refusal of another to arbitrate under a written agreement for arbitration may petition any United States district court ... for an order directing that such arbitration proceed in the manner provided for in such agreement.... The court shall hear the parties, and upon being satisfied that the making of the agreement for arbitration or the failure to comply therewith is not in issue, the court shall make an order directing the parties to proceed to arbitration in accordance with the terms of the agreement. ... If the making of the arbitration agreement or the failure, neglect, or refusal to perform the same be in issue, the court shall proceed summarily to the trial thereof.
This somewhat awkwardly phrased statute appears to pose for a court only the questions of whether there is an “issue” over “the making of [an] agreement for arbitration or the failure to comply therewith.” The latter question can usually be answered in the negative with a minimum of effort, since the parties are usually in court because one of them refuses to arbitrate a dispute. But the question whether there is an issue as to the making of an agreement to arbitrate is deceptively simple since it encompasses not only whether there was an agreement to arbitrate, but also whether the dispute falls within the scope of the arbitration clause and whether the agreement to arbitrate has been terminated. Cf. McAllister Brothers, Inc. v. A & S Transportation Co., 621 F.2d 519 (2d Cir.1980).
Section 12 of the collective bargaining agreement between the parties in this case covered strikes, lockouts, arbitration and grievances. The section provided, in relevant part, that “[no] employee shall be disciplined or discharged without just cause” and that “[a]ll disputes between the parties . .. which relate to the interpretation or application of [the] Agreement shall, if not resolved amicably ..., be referred to arbitration.” Thus, there is no doubt that at least until July 31, 1982, there was an agreement to arbitrate disputes between the parties. However, the Company argues that it was not obligated to arbitrate the discharges here because they occurred after the termination of the collective bargaining agreement on July 31, 1982. The Union argues that the grievance regarding the three employees arose on or before that date and is, therefore, an arbitrable dispute under the labor agreement.
We agree with the Union that the dispute between the parties is arbitrable. The underlying question is whether the Company had the right under the contract to require the employees to take a polygraph test or face the threat of discharge if they did not. The discovery of the theft under circumstances implicating employees, the request that the three grievants take the polygraph test, their refusal and the Company’s notice of its intention to discharge them if they adhered to their stated positions, all occurred prior to August 1, 1982. At oral argument to us, the Company’s counsel stated that there was nothing to show that the grievants received the Company’s letter on or before July 31,1982. The record is to *482the contrary. The Company’s petition to stay arbitration says that “[o]n July 28, 1982” it “notified the three individuals,” and in the district court, Company counsel stated to Judge Weinstein that “[t]he exact date of the receipt of this notice is unclear but I understand it was around July 31st.” In addition, the Union’s answer and counter-application allege that even before the letter was sent, to wit, on July 27, the question of bargaining about employees being forced to take polygraph tests was raised at the first collective bargaining session for a new contract.
Under these circumstances, we believe this case is governed by Nolde Brothers, Inc. v. Local No. 858, Bakery & Confectionery Workers Union, 430 U.S. 243, 97 S.Ct. 1067, 51 L.Ed.2d 300 (1977). In that case the Court required an employer to arbitrate a dispute over severance pay caused by a plant closing, even though the closing occurred four days after the collective bargaining agreement had terminated. The Court stated:
The parties agreed to resolve all disputes by resort to the mandatory grievance-arbitration machinery established by their collective-bargaining agreement. The severance-pay dispute, as we have noted, would have been subject to resolution under those procedures had it arisen during the contract’s term. However, even though the parties could have so provided, there is nothing in the arbitration clause that expressly excludes from its operation a dispute which arises under the contract, but which is based on events that occur after its termination. The contract’s silence, of course, does not establish the parties’ intent to resolve post-termination grievances by arbitration. But in the absence of some contrary indication, there are strong reasons to conclude that the parties did not intend their arbitration duties to terminate automatically with the contract.
430 U.S. at 252-53,97 S.Ct. at 1072-73. We believe that this reasoning applies equally to this case. Here, too, the parties agreed to submit to arbitration “all disputes” relating to the interpretation or application of the agreement. Here, too, there is no exclusionary language in the arbitration clause. And here, too, the claim has been asserted “within a reasonable time after the contract’s expiration.” See 430 U.S. at 255 n. 8, 97 S.Ct. at 1074 n. 8. Indeed, this is a stronger case for arbitrability than Nolde since the basic dispute over the employer’s right to compel a polygraph test clearly arose before the contract terminated. This distinguishes Proctor & Gamble Independent Union v. Proctor & Gamble Manufacturing Co., 312 F.2d 181 (2d Cir.1962), cert. denied, 374 U.S. 830, 83 S.Ct. 1872, 10 L.Ed.2d 1053 (1963), relied on by the Company. Cf. Ottley v. Sheepshead Nursing Home, 688 F.2d 883 (2d Cir.1982). It is true that the Union cast its demand for arbitration on the discharge and not on the giving of the notice on July 28. It is also true that the discharge itself, rather than the threat to do so, occurred after contract termination. But this does not render the dispute non-arbitrable, although it may affect the scope of the arbitrator’s remedy.
Accordingly, we affirm the judgment of the district court.
. The letter, which was written on Company stationery and was signed by the Company’s general counsel, read as follows:
CERTIFIED MAID — RETURN RECEIPT
July 28, 1982
Mr. Ralph Kendrick
9 Washington Place Patchoge [sic], NY 11772
Dear Mr. Kendrick:
As you are aware, on Saturday, July 17, 1982 a theft occurred in the offices of Glover Bottled Gas Corp. The sum of $1,947.81 in checks and $439.25 in cash was taken from the desk of Mrs. Lodato.
The police, in investigating the case, have determined that there were 5 possible suspects. The investigating officer has also determined that (a) the theft could not have been perpetrated by an outsider and (b) that the only means of further investigation open to the police was submission of the suspects [sic] a polygraph test.
The company has been advised that you have declined to submit to such a polygraph test. We are writing to you to afford you the opportunity of reconsideration.
We view the refusal of an employee to cooperate in an investigation by the public authorities into any form of theft, embezzlement or destruction of the company’s property, in general, or to refuse to participate in a polygraph examination where deemed appropriate by the investigating persons, in particular, as an extreme dereliction of duty, and an attempt to shielf [sic] the guilty party. Accordingly, unless on or before August 4, 1982 the company has received from you, in writing, a statement that you have reconsidered your position and will make yourself available for a polygraph examination in regard to the above described occurrence, you will be discharged.
Very truly yours,
Glover Bottled Gas Corp.
/s/ Daniel M. Shientag,
Daniel M. Shientag,
General Counsel DMS:cs