Reinsurance is not new. See People ex rel. Sea Ins. Co. v. Graves, 274 N.Y. 312, 315, 8 N.E.2d 872, 873-74 (1937). It dates back to the time the first bookie, fearful that he could not cover all his bets in the event he were to lose, decided to spread his risk by “laying-off’ some of the risks by getting other bookies to share his exposure. In a more respectable vein, reinsurance is a device whereby an insurance company that has assumed uncomfortable levels of risk buys insurance from another insurance company to assume some of those risks. Id. The basic insurer is then referred to as the “reinsured” or, sometimes as the “ceding insurer.” The reinsurer is called precisely that. By contract, the reinsurer agrees to assume some or all of the risk that the ceding insurer has assumed. Id.
Continental Casualty Company (“Continental”) in this case is the ceding insurer. It issued many liability policies to hospitals. It then laid off some of these risks to several reinsurance companies (the “reinsurers”)— defendants in this action. In the 1980’s, Continental paid out substantial sums to settle a spate of medical malpractice suits that had been brought against hospitals covered *18by Continental policies. Several years later, Continental turned to its reinsurers to get reimbursement. The reinsurers refused to pay.
Continental sued the reinsurers in the United States District Court for the Southern District of New York (Leonard B. Sand, Judge). After some procedural skirmishing, the reinsurers asserted a statute of limitations defense, posing a deceptively simple question: Under New York law, when does a cause of action for indemnity promised in a reinsurance policy accrue?
The reinsurers argued that Continental’s cause of action accrued the day it made payment on its underlying insurance policies, because at that moment it became entitled to indemnity. Even if the reinsurance policies required that Continental make a demand for payment as a precondition to liability under the reinsurance policies, the cause of action accrued when Continental was entitled to make the demand, and that would still be the day it made payments on the underlying-policies. Cf. N.Y.Civ.Prac.L. & R. 206(a) (McKinney 1990) (“CPLR 206(a)”).
Continental countered that its cause of action could not accrue until the reinsur-ers “breached” the reinsurance policies by refusing to indemnify Continental for its payments. It brushed aside CPLR 206(a), noting that section 206(a) applies only to “procedural” demands {e.g., the demand upon the Board of Directors as a condition to bringing a shareholder derivative action) and not to cases when a demand and refusal are a substantive element of a cause of action, (e.g., a demand upon a bailee to return a chattel as a condition to making the bailee liable as a tortfeasor). Continental’s view was that the reinsurers were not in breach of their contracts until Continental made an actual demand for reimbursement and was rebuffed by the reinsurers. The district court sided with Continental on both counts in a published opinion, Continental Cas. Co. v. Stronghold Ins. Co., 866 F.Supp. 143 (S.D.N.Y.1994), and thereafter entered judgment against the reinsurers.
On appeal, the parties renew the same basic arguments. We hold that the causes of action accrued when the reinsured notified the reinsurers of its losses under the reinsurance policies and the reinsurers subsequently denied coverage.
I.
The facts are undisputed, and are fully set forth in the district court’s opinion. See id. at 144-45. We will summarize them briefly.
In the 1960’s, the reinsurers issued reinsurance policies to Continental. The policies reinsured several medical malpractice insurance policies that Continental had issued to hospitals and hospital associations. Each reinsurance policy expressly required Continental to report to the reinsurers any losses “as soon as practicable.”
In the 1980’s, Continental settled several claims made upon its malpractice insurance policies. Some time later (the record does not say when), it notified the reinsurers of these settlements, and demanded that they pay their share. On various dates between 1987 and 1990, the reinsurers refused to pay, consistently denying liability under the reinsurance policies.
In November 1991, more than six years after it settled the last of the claims on the underlying policies, Continental sued the reinsurers, alleging that the reinsurers breached the various reinsurance policies by refusing its demands for payment. The rein-surers denied most of Continental’s allegations, but, more importantly, asserted as an affirmative defense that Continental itself breached the reinsurance policies by giving the reinsurers late notice of the settlements.
In an unrelated case, the New York Court of Appeals handed down a decision undermining the reinsurers’ late notice defense. Unigard Sec. Ins. Co. v. North River Ins. Co., 79 N.Y.2d 576, 584 N.Y.S.2d 290, 594 N.E.2d 571 (1992). This led the parties to enter into a conditional stipulation: the rein-surers would move in the district court for summary judgment dismissing the claims on statute of limitations grounds; in exchange they waived all other defenses. The agreement provided that if the district court ruled the claims time-barred, judgment would be entered for the reinsurers. On the other *19hand, if the district court ruled that the claims were timely, and that ruling was affirmed on appeal, the reinsurers would pay certain amounts under the policies.
As stipulated, the reinsurers moved for summary judgment on their statute of limitations defense. The parties agreed that: (1) New York law controlled; (2) New York’s six-year statute of limitations applied; (3) Continental satisfied all conditions of the reinsurance policies; (4) Continental had paid its insureds more than six years before suing the reinsurers; but (5) Continental commenced suit within six years of the rein-surers’ earliest denial of its demands for indemnity. Opposing the motion, Continental submitted a copy of the basic terms of one of the reinsurance policies; the contents of the policy were not disputed.
The district court denied the reinsurers’ motion. Continental Cas. Co., 866 F.Supp. at 145-47. Reasoning that ordinary contract principles applied in determining when Continental’s claims accrued, id. at 145, the district court held that no breach of the reinsurance policies occurred until the reinsurers refused Continental’s request for reimbursement, id. at 145-46. Because this happened well within the six-year limitations period governing contract claims, N.Y.Civ.Prae.L. & R. 213(2) (1990), Continental’s claims were timely as a matter of law. Id. at 146.
By this time, three of the reinsurers were mired in insolvency proceedings in English courts, resulting in a stay of Continental’s suit as to those three. The remaining rein-surers moved for entry of a final judgment pursuant to Federal Rule 54(b). Finding that there was “no just reason for delay,” Fed.R.Civ.P. 54(b), the district court granted the reinsurers’ motion and entered a final judgment against the solvent reinsurers in the amounts stipulated under the settlement agreement. This appeal followed.
II.
On appeal, the reinsurers argue that the six-year period of limitations began to run when Continental settled and paid the malpractice claims covered by the underlying insurance policies. Since this occurred more than six years before Continental brought suit, the reinsurers conclude that the actions are time-barred. Continental counters, and the district court agreed, that the limitations period did not begin to run until the reinsur-ers breached the reinsurance policies, and that was when Continental’s demand for indemnity was rejected.
It is an elementary principle of New York law that the statute of limitations “begins to run once a cause of action accrues.” Aetna Life & Cas. Co. v. Nelson, 67 N.Y.2d 169, 175, 501 N.Y.S.2d 313, 316, 492 N.E.2d 386, 389 (1986); see N.Y.Civ.Prae.L. & R. 203(a) (“[t]he time within which an action must be commenced ... shall be computed from the time the cause of action accrued”). Reinsurance policies are express contracts for indemnity against loss. See, e.g., In re Midland Ins. Co., 79 N.Y.2d 253, 258, 582 N.Y.S.2d 58, 60, 590 N.E.2d 1186, 1188 (1992) (“A reinsurance contract is one in which a reinsurer agrees to indemnify a primary insurer for losses it pays to its policyholders.”); see also Restatement of Security § 82 cmt. 1 (1941) (“indemnity is synonymous with insurance”). As such, the claim generally accrues when the indemnitee actually suffers a loss. See Steen v. Niagara Fire Ins. Co., 89 N.Y. 315, 325 (1882) (generally, the statute of limitations “begin[sj to run upon a contract of indemnityfl from the time at which the plaintiff is actually damaged”); Travelers Indemnity Co. v. LLJV Dev. Corp., - A.D.2d -,-, 635 N.Y.S.2d 179, 183 (1st Dep’t 1995) (“it is well settled that a cause of action based upon a contract of indemnification does not arise until liability is incurred by way of actual payment”).
An express contract for indemnity, however, remains a contract. Hence the parties are free, within limits of public policy, to agree upon conditions precedent to suit. See Proc v. Home Ins. Co., 17 N.Y.2d 239, 242-45, 270 N.Y.S.2d 412, 413-15, 217 N.E.2d 136, 137-38 (1966) (insured’s cause of action under policy did not accrue until it satisfied various conditions); Steen, 89 N.Y. at 322 (absent provisions to contrary in fire insurance policy, “a suit would have lain upon the instant of the happening of the fire, or within a reasonable time thereafter”); see also 46A *20C.J.S. Insurance § 1544 (1993) (“[i]n the absence of a contractual or statutory provision to the contrary, an action on a policy of insurance may be brought immediately on the happening of the loss”). Common conditions include filing proofs of loss and allowing the insurance company time to investigate and pay the claim. See Proc, 17 N.Y.2d at 242-43, 270 N.Y.S.2d at 413-14, 217 N.E.2d at 137-38. Thus, the rule has evolved in insurance cases that the cause of action accrues “when the loss insured against becomes due and payable” under the policy. Steen, 89 N.Y. at 324; 44 Am.Jur.2d Insurance § 1884, at 886 (1982); see 46A C.J.S. Insurance § 1554. We see no reason not to apply the “due and payable” insurance rule to reinsurance policies; reinsurance, after all, is simply insurance for insurance companies. Colonial Am. Life Ins. Co. v. Commissioner, 491 U.S. 244, 246-47, 109 S.Ct. 2408, 2411, 105 L.Ed.2d 199 (1989); People ex rel. Continental Ins. Co. v. Miller, 177 N.Y. 515, 521, 70 N.E. 10, 12 (1904) (“Reinsurance is a contract by which one insurer insures the risks of another insurer.”).
The timeliness of Continental’s claims thus turns on a fairly simple question: when were its losses due and payable under the reinsurance policies? The representative policy offered by the parties is hardly a paragon of clarity. But, we are able to discern at least one condition that Continental had to satisfy before its right to indemnity could mature. “Loss, if any, under” the policy is “to be reported to [the reinsurer] as soon as practicable.” Policy No. K. 76590 at ¶ 9 (J.A. at 100a). Because the reinsurers are then “liable only for the excess of loss” incurred by Continental over various specified amounts of “ultimate net loss,” id. at ¶ 2 (J.A. at 99a), and because “ultimate net loss” means “the sums actually paid in cash in settlement of losses [for] which [Continental] is liable,” id. at ¶ 4 (J.A. at 100a), we construe the notice provision to mean that Continental had to report any actual losses — ie., payments made on its underlying insurance policies — within a reasonable period of time under the circumstances. Cf. Christiania Gen. Ins. Corp. v. Great Am. Ins. Co., 979 F.2d 268, 275 (2d Cir.1992). We also conclude that Continental was entitled — indeed probably obligated — to wait a reasonable time for the reinsurers to decide whether they would pay or not, and, if so, how much. See Restatement (Second) of Contracts §§33 cmt. d, 204 cmt. d (1981).
Unigard is not to the contrary. There, the New York Court of Appeals faced a reinsurance policy provision requiring notice of potential, as opposed to actual, losses. Thus the reinsured had to give “ ‘[p]rompt notice ... of any occurrence or accident which appears likely to involve this reinsurance.’ ” Unigard, 79 N.Y.2d at 579, 584 N.Y.S.2d at 291, 594 N.E.2d at 572 (quoting the reinsurance policy). The court held that, unlike cases involving ordinary insurance, e.g., Security Mut. Ins. Co. v. Acker-Fitzsimons Corp., 31 N.Y.2d 436, 440, 340 N.Y.S.2d 902, 905, 293 N.E.2d 76, 78 (1972), failure to comply with this provision was not an absolute defense to the reinsurer’s liability under the policy, because the provision was not an express condition precedent. Unigard, 79 N.Y.2d at 581-82, 584 N.Y.S.2d at 292-93, 594 N.E.2d at 573-74. Rather, to escape liability because of a late notice, the reinsurer had to show prejudice. Id. at 584, 584 N.Y.S.2d at 294, 594 N.E.2d at 575. Underlying Unigard was the court’s recognition that “failure to give the required prompt notice is of substantially less significance for a reinsurer than for a primary insurer.” Id. at 583, 584 N.Y.S.2d at 293, 594 N.E.2d at 574.
It should be emphasized that Unigard addressed only the prejudice — or lack thereof — caused by late notice of potential losses; it said nothing about when the reinsured’s actual losses under the policy were due and payable. See Unigard, 79 N.Y.2d at 578-84, 584 N.Y.S.2d at 290-94, 594 N.E.2d at 571-75 (repeatedly casting issue as the consequence of reinsured’s failure to give prompt notice of potential claims). Assuming Unigard applies here at all, it stands only for the proposition that the reinsurers cannot escape liability simply because Continental tarried before advising them that hospitals were making claims on the underlying policies. It would distort Unigard to read it as meaning that the reinsurers had a duty to indemnify Continental even before Continental gave notice of *21the payments it had made to the hospitals. See Barry R. Ostrager & Thomas R. Newman, Handbook on Insurance Coverage Disputes § 15.04[b], at 680 (8th ed.1995). Under these policies, Continental’s actual losses were not due and payable until a reasonable period of time elapsed after it gave notice of them. Accordingly, Continental’s causes of action accrued then (or when the reinsurers refused to pay, if earlier), and not before.
III.
CPLR 206(a) is no impediment to Continental’s claims. Under that statute, “where a demand is necessai-y to entitle a person to commence an action, the time within which the action must be commenced [generally] shall be computed from the time when the right to make the demand is complete.” N.Y.Civ.Prac.L. & R. 206(a). Relying on the purportedly “plain” meaning of this language, the reinsurers argue that because Continental could have “demanded” indemnity by giving notice of the claims as soon as it paid them, its causes of action accrued as soon as it paid the underlying malpractice settlements. We disagree.
New York courts do not instinctively apply CPLR 206(a) in every case where a demand is a predicate to suit. Rather, they distinguish between substantive demands and procedural demands. See Dickinson v. Mayor of Ne%v York, 92 N.Y. 584, 591 (1893) (construing § 206(a)’s statutory predecessor); Kunstsammlungen zu Weimar v. Elicofon, 678 F.2d 1150, 1161 (2d Cir.1982); see generally 1 Jack B. Weinstein et al., Neiv York Civil Practice ¶ 206.01 (1995). This distinction derives from earlier statutes, which CPLR 206(a) merely rephrased, see 2 N.Y.Adv.Comm.Rep. 53 (1958), and which expressly applied only “ ‘where a right exists, but a demand is necessary to entitle a person to maintain an action.’ ” 1 Weinstein, supra, ¶ 206.01, at 2-241 (quoting statutory predecessors to § 206(a)).
Thus, where a demand is an essential element of the plaintiffs cause of action, as in bailment cases, see, e.g., Ganley v. Troy City Nat’l Bank, 98 N.Y. 487, 493-96 (1885), and replevin cases involving good-faith purchasers of stolen ait, see, e.g., Solomon R. Guggenheim Found, v. Lubell, 77 N.Y.2d 311, 319, 567 N.Y.S.2d 623, 627, 569 N.E.2d 426, 430 (1991), CPLR 206(a) does not apply. Similarly, here a “demand,” in the form of notice to the reinsurers of actual losses on the underlying insurance policies, is an essential element of Continental’s indemnity claims. As we have made clear, Continental had no right to indemnity under the policies until it satisfied this provision. And, the reinsurers were not in “breach” of their contract to indemnify until they rejected the demand (or until a reasonable time for paying the losses elapsed). Accordingly, CPLR 206(a) does not apply.
We of course recognize that a plaintiff should not “have the power to put off the running of the Statute of Limitations indefinitely.” Snyder v. Town Insulation, Inc., 81 N.Y.2d 429, 435, 599 N.Y.S.2d 515, 518, 615 N.E.2d 999, 1002 (1993); see 18 Samuel Willi-ston, Law of Contracts, § 2021A, at 697 (Walter H.E. Jaeger ed., 1978) (“[w]here the plaintiffs right of action depends upon a preliminary act to be performed by himself he cannot suspend indefinitely the running of the Statute of Limitations by delaying performance of this act”); see also Developments in the Law — Statutes of Limitations, 63 Harv.L.Rev. 1177, 1209 (1950). Thus, once Continental suffered losses on the underlying policies, it could not unreasonably delay reporting those losses to the reinsur-ers. Cf. Solomon R. Guggenheim Found., 77 N.Y.2d at 319, 567 N.Y.S.2d at 627, 569 N.E.2d at 430 (“the true owner, having discovered the location of its lost property, cannot unreasonably delay making demand upon the person in possession of that property”). But, by abandoning the late notice defense and by actually stipulating that Continental satisfied all conditions of the policies, including the notice provision, the reinsurers have conceded that no unreasonable delay happened here.
IV.
Although it has been said that the relationship between a reinsured and its reinsurer is not technically a fiduciary one, see Christia-na Gen. Ins. Corp. v. Great Am. Ins. Co., 745 *22F.Supp. 150, 161 (S.D.N.Y.1990), centuries of history have treated both as allies, rather than adversaries. See Unigard, 79 N.Y.2d at 583, 584 N.Y.S.2d at 293, 594 N.E.2d at 574. It is customary, for example, for both to share the premium paid by the underlying insured for coverage. See, e.g., In re Midland Ins. Co., 79 N.Y.2d at 258, 582 N.Y.S.2d at 60, 590 N.E.2d at 1188. Often they jointly prepare and defend unfounded claims by overreaching insureds. See, e.g., Unigard, 79 N.Y.2d at 583-84, 584 N.Y.S.2d at 294, 594 N.E.2d at 575 (reinsurer’s “ ‘right to associate’ involves the right to consult with and advise the reinsured in its handling of a claim”).
Because custom and usage have established a gentility and unity of interest between the reinsured and its reinsurer, cf. Sumitomo Marine & Fire Ins. Co. v. Cologne Reins. Co., 75 N.Y.2d 295, 298, 552 N.Y.S.2d 891, 892, 552 N.E.2d 139, 140 (1990) (reinsurance is “a field in which differences have often been settled by handshakes and umpires”), a generation ago, we doubt that the defendants would even have considered asserting a statute of limitations defense. See Ronald C. King, Limitation of Action Considerations in Respect of U.K. Insurers, 61 Def.Couns.J. 226, 226 (1994) (“Defences based on available periods of limitation usually have not been taken by insurers in the London market, and some participants in the market feel that it is a custom not to assert them.”). With the collapse of prominent British reinsurers, and the financial distress of Lloyd’s of London, times may have changed. Id. at 226, 231; see also Unigard Sec. Ins. Co. v. North River Ins. Co., 4 F.3d 1049, 1054 (2d Cir.1993). As Francois Villon sighed: Oú sont les neiges d’antan? (“Where are the snows of yesteryear?”).
In any event, consistent with longstanding New York precedent, we hold that, on these facts, Continental’s losses were due and payable, and its causes of action accrued, only after it reported the losses to the reinsurers, and the reinsurers denied coverage. Accordingly, the judgment is AFFIRMED.