FAGG, Circuit Judge.

In November 1987 Stifel, Nicolaus Company (Stifel), a securities brokerage firm, brought a diversity action against customers Ronald G. Freeman and Beverly Freeman Weyhmueller to recover outstanding debit balances in their accounts. Freeman and Weyhmueller filed an amended counterclaim in February 1988, asserting Stifel mishandled the accounts in violation of the Securities Act of 1933 (1933 Act), 15 U.S.C. § 77a-77aa (1988), the Securities Exchange Act of 1934 (1934 Act), 15 U.S.C. § 78a-78 ll (1988), and Missouri law. Stifel did not assert arbitration as an affirmative defense in its reply to the amended counterclaim. The parties engaged in written discovery. Later, in May 1988, Stifel moved to compel arbitration of the entire lawsuit. See 9 U.S.C. § 3, 4 (1988). The district court granted Stifel's motion and dismissed the action without prejudice. Freeman and Weyhmueller appeal, and we affirm.

Freeman opened two accounts with Stifel: one for himself and one for a general partnership comprised of Freeman, Weyhmueller, and a third person. When Freeman opened the accounts, he signed an options agreement and a customer's agreement for each. The options agreements provide the parties will arbitrate all controversies except those "for which a remedy may exist pursuant to an express or implied right of action under the federal securities laws." The customer's agreements provide the parties will arbitrate all controversies except those for which "waiver of the right to seek a judicial forum . . . would be void under the federal securities laws." Freeman and Weyhmueller contend they did not agree to arbitrate their federal securities laws claims.

We agree with the district court that the customer's agreements require arbitration of Freeman and Weyhmueller's federal securities laws claims. See Rodriguez de Quijas v. Shearson/American Express, 490 U.S. 477, 479-84, 109 S.Ct. 1917, 1919-21, 104 L.Ed.2d 526 (1989) (1933 Act); Shearson/American Express v. McMahon, 482 U.S. 220, 234, 238, 107 S.Ct. 2332, 2341, 2343, 96 L.Ed.2d 185 (1987) (1934 Act). We need not decide whether the options agreements exclude arbitration of federal securities laws claims because the customer's agreements provide they supersede any contemporaneously executed agreements to the extent there is a conflict between the instruments. Thus, the parties agreed to arbitrate all their claims, including those based on federal securities laws.

Freeman and Weyhmueller also argue Stifel waived its contractual right to arbitration under the agreements. We review the question of waiver de novo. Ackerberg v. Johnson, 892 F.2d 1328, 1332 (8th Cir. 1989). Accordingly, we must determine whether Stifel voluntarily relinquished a known right to arbitration. Id.

To prove Stifel waived its right to arbitration, Freeman and Weyhmueller must show: (1) Stifel knew of an existing right to arbitration; (2) Stifel acted inconsistently with that right; and (3) Stifel's inconsistent acts prejudiced them. Fisher v. A.G. Becker Paribas Inc., 791 F.2d 691, 694 (9th Cir. 1986); see also Nesslage v. York Sec., Inc., 823 F.2d 231, 234 (8th Cir. 1987). When considering these factors, we will "resolve in favor of arbitration `any doubts concerning . . . [the] allegation of waiver.' " Phillips v. Merrill Lynch, Pierce, Fenner Smith, 795 F.2d 1393, 1397 n. 9 (8th Cir. 1986) (quoting Moses H. Cone Memorial Hosp. v. Mercury Const. Corp., 460 U.S. 1, 24-25, 103 S.Ct. 927, 941-942, 74 L.Ed.2d 765 (1983)); see also Nesslage, 823 F.2d at 234.

The parties do not dispute that Stifel knew of its existing right to compel arbitration of all claims, including those under the 1933 Act and the 1934 Act. Nevertheless, Freeman and Weyhmueller assert Stifel acted inconsistently with this right to their prejudice when it filed the original lawsuit, engaged in discovery on arbitrable claims, and failed to move to compel arbitration until six months after the suit was filed. We agree that Stifel acted inconsistently with its right to arbitration by initiating litigation and participating in discovery on arbitrable claims. See Ackerberg, 892 F.2d at 1331. We do not agree, however, that Stifel's actions prejudiced Freeman and Weyhmueller.

Whether inconsistent actions constitute prejudice is determined on a case-by-case basis. Prudential-Bache Sec. v. Stevenson, 706 F. Supp. 533, 536 (S.D.Tex. 1989). Prejudice may result from lost evidence, duplication of efforts, use of discovery methods unavailable in arbitration, id. at 535, or litigation of substantial issues going to the merits, Rush v. Oppenheimer Co., 779 F.2d 885, 887 (2d Cir. 1985). Additionally, a party's failure to assert a prelitigation demand for arbitration may contribute to a finding of prejudice because the other party has no notice of intent to arbitrate. Prudential-Bache, 706 F. Supp. at 535. Delay in seeking to compel arbitration does not itself constitute prejudice. Rush, 779 F.2d at 887.

Applying these factors to this case, we conclude Freeman and Weyhmueller were not prejudiced; thus, Stifel did not waive its contractual right to arbitration. Although Stifel invoked the judicial process and there was some pretrial litigation activity, primarily pleadings and discovery, no issues were litigated and the limited discovery conducted will be usable in arbitration. In our view, the fact that Stifel initiated litigation to recover debit balances and waited three months after Freeman and Weyhmueller filed their amended counterclaim for violations of federal securities laws before moving to compel arbitration did not prejudice Freeman and Weyhmueller. See id. at 887-89.

We affirm the district court's orders compelling arbitration and dismissing this action.