Plaintiff-Appellant Cecil L. Archer, a disabled pilot, sued his union, defendant-appel-lee Air Line Pilots Association International (ALPA), under the Railway Labor Act, 45 U.S.C. § 151 et seq., for allegedly breaching its duty of fair representation by failing to process properly Archer’s insurance grievance. The district court granted summary judgment in ALPA’s favor. We affirm.

On March 13, 1969, Braniff Airways, Inc., Archer’s employer, and ALPA signed a Letter of Agreement which provided that Braniff would make available to its pilots specified amounts of group insurance coverage. Pursuant to this agreement, Braniff secured several group policies from Connecticut General Life Insurance Company. Braniff paid the premium for the basic life insurance policy, under the terms of which $10,000 was payable upon the death or disability of a pilot. In addition to the basic coverage, pilots were given the option of obtaining supplemental life and disability insurance at their own expense. Archer alleges that he filed timely applications for a $40,000, supplemental life insurance policy and a $1,500 per month disability insurance policy. On April 20, 1969, Archer was hospitalized; he subsequently became totally disabled and retired from Braniff’s service. He filed a claim for the $10,000 basic coverage, the $40,000 supplemental coverage, and the $1,500 per month disability benefits. Connecticut General refused to pay more than $10,000, contending that supplemental life insurance policy’s face amount was payable only in the event of the pilot’s death, not his disability, and that Archer was ineligible for disability benefits because he had not submitted his enrollment form on time.

Instead of filing a grievance against Braniff, whose duty it was to ensure that pilots received the coverage promised them by the March 13,1969 Letter of Agreement, Archer complained to ALPA. The union investigated Archer’s complaint, and on July 30, 1971, it informed him that no action would be taken. ALPA advised Archer that two potential avenues for seeking redress were open to him: filing a grievance against Braniff and suing Connecticut General. Despite this formal rejection of his request for assistance, Archer continued to press the union to “handle his grievance.” A union official made certain enquiries on Archer’s behalf, but by March 1972 it was clear that ALPA considered Archer’s case closed.

On May 16, 1972, Archer entered into a contingent fee arrangement with a private attorney, paid him a $500 retainer, and authorized him to sue Braniff and Connecticut General. Such a suit was filed in the United States district court on March 28, 1973. On April 15, 1975, the defendants settled the case by paying Archer the full amount of the benefits he had requested ($77,-283.63). Pursuant to the contingent fee contract, Archer paid his attorney $30,-913.45. He also incurred court costs of $92.

On June 16,1975, Archer filed the instant action against ALPA. He charges the union with having “breached its duty of fair representation by handling the plaintiff’s insurance grievances with BRANIFF, and its insurer in an arbitrary, discriminatory, and bad faith manner” as a result of which “plaintiff incurred damages (attorney’s fees and court costs) when he retained a private attorney to process his insurance grievances against his employer, BRANIFF, and its insurer.” An amended complaint was filed on October 25, 1975. ALPA moved for summary judgment on the grounds that: (1) Archer’s action was barred by the statute of limitations; and (2) Archer failed to state a valid claim. In support of the second ground, ALPA argued that it was under no legal obligation to handle Archer’s insurance grievance, and claimed that even if such a duty was owed, there existed no genuine issue as to any material fact pertaining to the adequacy of its performance of that duty. Without stating the ground on which it relied, the district court granted summary judgment in ALPA’s favor. Archer then took this appeal.

I

We address ourselves first to the statute of limitations question. Archer is a resident of California; all of the relevant events occurred in California; and California is the forum state. Therefore, the applicable statute of limitations is Cal.Civ.Pro. Code § 338, which requires that “an action upon a liability created by statute, other than a penalty or forfeiture” be commenced within three years. Price v. Southern Pacific Trans. Co., 586 F.2d 750 , 752-53 (9th Cir. 1978). Although state law defines the length of the limitations period, federal law determines when the plaintiff’s alleged cause of action accrued. Id. at 754. To identify the time of accrual, courts look to (1) the date on which the last “action by the Union of any consequence occurred”; and (2) “the point at which any injury to [the union member] allegedly caused by the Union became fixed and reasonably certain.” Id.

ALPA’s last official act occurred in July 1971 and its last unofficial act in March 1972. Interpreting the facts in the light most favorable to Archer, we consider the latter the final action “of any consequence.” On May 16, 1972, only a few weeks after the union closed its files on Archer’s insurance complaint, he suffered a “fixed and reasonably certain” injury in the amount of $500, the sum he paid to his attorney. At that time, it also became apparent that he would suffer further monetary injuries in the form of court costs. The general rule is that, where it is possible to prove the extent of future injuries without resorting to undue speculation, the cause of action for those injuries is deemed to have accrued when the wrongful act occurred. See Zenith Radio Corp. v. Hazeltine Research, Inc., 401 U.S. 321, 339 , 91 S.Ct. 795 , 28 L.Ed.2d 77 (1971). Thus, Archer’s cause of action against ALPA for reimbursement of the $500 retainer and the $92 in court costs accrued in March 1972. Because Archer did not file suit against ALPA until June 16, 1975, more than four years after the accrual date, the retainer and court costs claims were time-barred.

Archer’s contingent fee reimbursement claim was not time-barred, however. Where future damages are too speculative to prove at the time the defendant’s wrongdoing takes place, “the cause of action for future damages, if they ever occur, will accrue only on the date they are suffered.” Id. at 339 , 91 S.Ct. at 806 . Under this rule, “an accrual of damages can constitute the accrual of a cause of action even though all wrongful acts took place outside the limitations period.” In Re Multidistrict Vehicle Air Pollution, 591 F.2d 68, 72 (9th Cir. 1979). But the plaintiff’s recovery is restricted to damages that accrued during the applicable limitations period. See Hanson v. Shell Oil Co., 541 F.2d 1352, 1361 (9th Cir. 1976), cert. denied, 429 U.S. 1074 , 97 S.Ct. 813 , 50 L.Ed.2d 792 (1977). The contingent fee contract provided that Archer’s attorney would receive a percentage of any sums received from Connecticut General and Braniff. Until settlement was reached on April 15, 1975, it was impossible to estimate the amount Archer would eventually owe his counsel; the size of the fee could have ranged anywhere from zero to tens of thousands of dollars. Had Archer sued ALPA for reimbursement of the contingent fee at any time prior to April 15, 1975, his suit undoubtedly would have been dismissed on the ground that the damages sought were unduly speculative. Given these circumstances, Archer’s cause of action for reimbursement of the contingent portion of his attorney’s fee accrued on the date when the fee became “fixed and reasonably certain,” April 15, 1975, which was only two months before the instant suit was filed.

We hold that the three-year statute of limitations furnished an adequate basis for granting summary judgment in ALPA’s favor only as to Archer’s cause of action for recovery of the retainer and court costs. The statute did not justify summary judgment on the contingent fee reimbursement claim.

II

Now we must ask whether the other ground asserted by ALPA — failure to state a claim — warranted summary judgment against Archer on the contingent fee reimbursement issue. To state a good cause of action, Archer had to allege that ALPA owed him a duty to process his grievance in accordance with the standards of the fair representation doctrine, that ALPA breached that duty, and that as a consequence he had to pay the contingent fee. If the pleadings, depositions, answers to interrogatories, admissions on file, and affidavits showed that ALPA owed no duty of fair representation under these circumstances, ALPA was entitled to judgment as a matter of law regardless of the nature of its conduct.

In the recent case of International Brotherhood of Workers v. Foust,-U.S.-, 99 S.Ct. 2121, 2125 , 60 L.Ed.2d 698 (1979), the Supreme Court described a labor union’s duty of fair representation in these terms:

See also Ness v. Safeway Stores, Inc., 598 F.2d 558 (9th Cir. 1979); Franklin v. Southern Pacific Trans. Co., 593 F.2d 899 (9th Cir. 1979); Robesky v. Quantas Empire Airways Ltd., 573 F.2d 1082 (9th Cir. 1978); Dente v. International Org. of Masters, Mates and Pilots, Local 90, 492 F.2d 10 (9th Cir. 1973), cert. denied, 417 U.S. 910 , 94 S.Ct. 2607 , 41 L.Ed.2d 214 (1974).

Archer’s argument founders because ALPA did not owe him a duty of fair representation. As Foust makes clear, the statutory duty of fair representation arises when by statute the union is the employees’ exclusive bargaining agent with the employer. 99 S.Ct. at 2125 . The doctrine protects against arbitrary union conduct against employees when the union provides the employees’ only redress against the employer. Id.

Archer’s grievance against Connecticut General is a different matter. ALPA was not statutorily empowered to provide redress for Archer’s grievance against Connecticut General. Nor did the ALPA-Braniff collective bargaining agreement provide that ALPA would be the employees’ exclusive bargaining agent with Connecticut General. The bargaining agreement required Braniff to obtain insurance for its employees, but it neither set up procedures for making insurance claims nor made ALPA the exclusive vehicle for pursuing grievances. Archer was not required, under the terms of the agreement, to first exhaust procedures provided in the agreement before resorting to the courts. Indeed, he brought suit directly in the district court and has cited other cases where other pilots, union members of ALPA, brought suit. Myre v. Connecticut General Life Insurance Co., 501 F.2d 609 (8th Cir. 1974); Moore v. Connecticut General Life Insurance Co., 277 So.2d 839 (Fla.App.1973), cert. denied, 291 So.2d 204 (Fla.1974). It is clear that ALPA had no duty to fairly represent Archer’s grievance against Connecticut General.

Archer contends however, that “assuming arguendo that ALPA owed no legal duty of fair representation to ARCHER vis-a-vis his insurance claims, it, nonetheless, became subject to this fiduciary duty once it made representations, upon which appellant relied, that it would investigate his claim.” This estoppel argument is without merit. Even if Archer did rely upon ALPA to process his grievance, his reliance was unreasonable. Having served as one of ALPA’s representatives during negotiation of the collective bargaining agreement with Braniff, Archer knew or should have known that he had no right to expect ALPA to handle his case in a particular manner until he had filed a grievance in accordance with section 37 of the contract.

In conclusion, we hold that, with regard to Archer’s contingent fee reimbursement claim, summary judgment in favor of ALPA was proper because ALPA did not owe Archer a legal duty.

The judgment of the district court is AFFIRMED.