Appellant Kroger Company had a collective bargaining agreement with appellee, the United Industrial Workers, Service, Transportation, Professional and Government of North America, Atlantic, Gulf Lakes and Inland Waters District, AFL-CIO (“UIW”). In 1987, Kroger transferred some work done by the UIW to the United Pood and Commercial Workers District Union, Local 1059 (“UFCW”), a union with which Kroger also had a collective bargaining agreement. The UIW filed a grievance with Kroger, followed the grievance procedures of the collective bargaining agreement between it and Kroger, and requested binding arbitration over the work assignment. Kroger invited the UFCW to join this arbitration voluntarily, contending that the UFCW was a necessary party to the proceeding, since the outcome of the proceeding could affect its right to perform the transferred work. Kroger did not file a formal grievance with the UFCW.
The UFCW refused to join the arbitration and, because of this refusal, Kroger subsequently refused to arbitrate with the UIW. The UIW sued in the United States District Court for the Northern District of Ohio to compel Kroger to arbitrate; Kroger interpled the UFCW to compel tripartite arbitration, citing Columbia Broadcasting System, Inc. v. American Recording and Broadcasting Association, 414 F.2d 1326 (2nd Cir.1969) (“CBS”).
The district court found that CBS did not require tripartite arbitration in this case, awarded summary judgment to the UIW, and dismissed the complaint against the UFCW. In particular, the district court found that CBS concerned the joinder of two pending arbitration proceedings, not the inclusion of a third party into one pending proceeding. Finding no error in the grant of summary judgment by the district court to the UIW, or the dismissal of Kroger’s third-party complaint against the UFCW, we now affirm.
I
On November 17, 1985, the Kroger Company entered into a collective bargaining agreement with the UIW which covered workers at a dry goods warehouse in Columbus, Ohio. Article 2.3 of the agreement provided:
... in the event The Kroger Co’s Columbus Marketing Area operates additional warehouse facilities in the greater Columbus area with its own employees for the distribution of products to its retail stores, the Union, pursuant to applicable law, will be recognized as the bargaining agent for that facility....
Article 5.2 provided in part:
Any differences, disputes or complaints arising over the interpretation or application of the terms of this Agreement shall be submitted within five (5) days to the Employer in writing, signed by the employee. There shall be an earnest effort on the part of both parties to settle such promptly through the following steps....
The article then listed four steps for the processing of grievances. Article 5.3 provided, in the event these steps did not resolve the grievance, that “the dispute may be submitted to arbitration by either party.” Further, the arbitrator’s decision “shall be binding on the employee and both *946parties.” Thus, under this collective bargaining agreement, one party could compel the other to engage in binding bipartite arbitration.
On February 14, 1988, Kroger entered into a new collective bargaining agreement with the UFCW, a union which represents employees at a meat plant in Columbus. The UFCW contract had a grievance procedure that also covered a broad range of disputes. The grievance procedure provided four steps; if, after completing the fourth step, the dispute is not settled, “... it shall be referred to the Board of Arbitration.” Thus, under this collective bargaining agreement as well, one party could compel the other to engage in binding bipartite arbitration.
Sometime in 1984, Kroger ceased some of its meat-processing operations at the UFCW-covered meat plant, which resulted in unused refrigerated space. The refrigerated area of the UIW-covered dry goods warehouse was filled to capacity. Around April or May 1987, Kroger transferred the handling of certain perishable items from the refrigerated portions of the dry goods warehouse to the refrigerated portions of the meat plant. UFCW members began to perform work at the meat plant in connection with these items.
On May 1, 1987, the UIW filed a grievance with Kroger, demanding that its members perform this work transferred to UFCW members. The grievance was processed through the steps of the grievance procedure in the collective bargaining agreement. In October 1987, the grievance reached the fourth step of this procedure. Kroger and the UIW were unable to resolve the grievance at this step, and an arbitrator was selected.
On February 15, 1988, Kroger asked the UFCW to join the arbitration proceeding voluntarily, but the UFCW refused. On the basis of the UFCW’s refusal, Kroger refused to arbitrate with the UIW, claiming that to engage in bipartite arbitration with the UIW alone might expose it to conflicting liability. Kroger filed no formal grievance with the UFCW under the collective bargaining agreement between it and the UFCW.
On May 2, 1988, the UIW sued Kroger in the United States District Court for the Northern District of Ohio to compel arbitration of this dispute under Section 301 of the Labor Management Relations Act of 1947. On June 24, Kroger filed an answer and a “Third-Party Complaint and Counterclaim in Interpleader”. Kroger named the UFCW as a third-party defendant. Kroger requested the court to order tripartite arbitration involving it, the UIW, and the UFCW. Both the UIW and Kroger moved for summary judgment.
On April 12, 1989, the court denied Kroger’s motion for summary judgment, dismissed the third-party complaint, and granted UIW’s motion for summary judgment. In part, the district court based its decision on the fact that Kroger had not filed a formal grievance under the collective bargaining agreement; it had merely requested that the UFCW participate voluntarily. The district court characterized the primary case cited by Kroger, Columbia Broadcasting System, Inc. v. American Recording and Broadcasting Association, 414 F.2d 1326 (2nd Cir.1969), as a ease concerning consolidation of pending arbitration proceedings. Since Kroger did not file a formal grievance against the UFCW, and thus had no pending arbitration proceeding with the UFCW, the district court had nothing to consolidate. Kroger appealed.
II
Based on the language of the collective bargaining agreement between Kroger and the UIW, it is clear that Kroger must engage in binding arbitration with the UIW. See United States Steelworkers v. Warrior & Gulf Navigation Co., 363 U.S. 574, 582-83, 80 S.Ct. 1347, 1352-53, 4 L.Ed.2d 1409 (1960). A possibility of external adverse consequences, such as exposure to inconsistent liabilities, cannot abrogate that duty. The only difficult issue before us is whether the UFCW may also be compelled to join that arbitration proceeding.
*947Before tripartite arbitration may be ordered, the parties involved first must have a duty to engage in separate bipartite arbitration over the subject matter involved. As the Ninth Circuit pointed out in United States Postal Service v. American Postal Workers Union:
For the district court to have the power to compel tripartite arbitration, a contractual nexus is required to both (a) the parties and (b) the subject matter.
893 F.2d 1117, 1120 (9th Cir.1990). We find that this necessary “contractual nexus” is lacking between Kroger and the UFCW.
Under the collective bargaining agreement, the UFCW has consented to binding bipartite arbitration with Kroger, but only as to issues on which a grievance has been filed and where the steps of the grievance procedure have been followed. Although some courts have suggested that this distinction is not meaningful, see, e.g., RCA Corp. v. Local Union 1666, 633 F.Supp. 1009, 1014 (E.D.Pa.1986), we disagree. Federal labor policy is that grievance procedures are integral parts of collective bargaining agreements. As the Supreme Court stated in United States Steelworkers v. Warrior & Gulf Navigation Co.,
[t]he processing of disputes through the grievance machinery is actually a vehicle by which meaning and content are given to the collective bargaining agreement.
The grievance procedure is, in other words, a part of the continuous collective bargaining process.
363 U.S. 574, 581, 80 S.Ct. 1347, 1352, 4 L.Ed.2d 1409 (1960). With this policy in mind, we hold that requiring the filing of a grievance prior to engaging in bipartite arbitration is not an empty formality.
Procedural questions of whether steps of a grievance procedure have been followed are generally left to the arbitrator. John Wiley & Sons v. Livingston, 376 U.S. 543, 557, 84 S.Ct. 909, 918, 11 L.Ed.2d 898 (1960). Substantive questions of whether an arbitrable grievance has been filed at all, however, are for the courts to decide. See AT & T Technologies, Inc. v. Communications Workers of America, 475 U.S. 643, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986). We find that Kroger’s mere request to the UFCW to engage in tripartite arbitration, absent more, does not constitute such a grievance under the collective bargaining agreement. It does not “claim a breach of the collective bargaining agreement.” Intern. Ass’n of Machinists and Aerospace Workers, Lodge 1000 v. General Electric Co., 865 F.2d 902, 905 (7th Cir.1989). Thus, Kroger cannot at this stage compel the UFCW to engage in bipartite arbitration, let alone tripartite arbitration.
Furthermore, holding that Kroger’s failure to file a grievance is irrelevant would essentially rewrite the collective bargaining agreement between it and the UFCW; as we have stated, the UFCW bargained for binding arbitration only as to issues on which a grievance has been filed. Although the UFCW and Kroger may fail to reach an amicable solution by following the pre-arbitration steps of the grievance procedure, such speculation cannot undermine the necessity of filing a grievance.
Ill
Another significant problem confronting us, one which neither the CBS nor the American Postal Workers Union court needed to address, is the potential for conflict between different collective bargaining agreements in the choice of arbitrators. In CBS, both unions agreed on a common arbitrator. 414 F.2d 1326, 1329 (2nd Cir.1969). Thus, that court noted, “... whatever difficulty might have plagued the court if there had been a disagreement among the parties on this point was and is obviated.” Ibid. Similarly, in the American Postal Workers Union case, the union attempting to intervene in the pending bipartite arbitration assented to the arbitrator already chosen. 893 F.2d at 1121. Thus, that court also noted that “[w]e are not faced with any procedural difficulties in this case,” ibid., referring to the problem of finding a suitable arbitrator.
*948We, however, are confronted with this problem. Under the collective bargaining agreement between the UIW and Kroger, a UIW representative and a Kroger representative shall request the Federal Mediation and Conciliation Service to provide a panel from which an arbitrator may be chosen by the two parties.” Under the agreement between the UFCW and Kroger, both parties
... shall request the Director of [sic] Federal Mediation and Conciliation Service to furnish a panel of seven (7) arbitrators from which the arbitrator shall be chosen, within fifteen (15) days from the date of the receipt of the panel, by the alternative striking of names. The fifteen (15) day limit for the selection of the Arbitrator and/or the date of the hearing may be extended and/or changed by mutual agreement of the two parties. The Employer and the Union shall decide who will strike first by flipping a coin.
This procedure clearly gives the UFCW certain rights in the selection of an arbitrator, rights which it was unable to exercise in the choice of an arbitrator for the dispute between Kroger and the UIW.
If the UFCW exercises its rights under its collective bargaining agreement, it can compel selection of an arbitrator other than the one chosen by Kroger and the UIW under their collective bargaining agreement. The problem of a conflicting choice of arbitrators is more than merely theoretical in this case. At oral argument, counsel for the UFCW indicated that the arbitrator already chosen in the pending Kroger/UIW arbitration would be unacceptable to the UFCW.
The UFCW would, in no respect, be bound by the decision of an arbitrator chosen in contravention of the procedure outlined in its collective bargaining agreement with Kroger, absent its consent. Avis Rent-a-Car Systems v. Garage Employees Union, 791 F.2d 22, 25 (2nd Cir.1986). If Kroger and the UFCW do engage in bipartite arbitration under the terms of their collective bargaining agreement, the arbitrator chosen could, in consultation with the arbitrator for the Kroger and UIW dispute, creatively fashion a remedy which both respects the agreement between Kroger and the UFCW and avoids conflicting with the decision rendered in the arbitration between Kroger and the UIW.
However, even under CBS, our power does not extend to forcing parties into types of arbitration that contradict their collective bargaining agreement. Accordingly, we refuse to compel the UFCW to engage in tripartite arbitration with the arbitrator chosen by Kroger and the UIW. The decision of the district court is AFFIRMED.