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36 Nos. 77-1698, 77-1210 & 77-1370 since the existence of multiple conspiracies is really a fact question as to the nature of the agreement, it is for the jury to decide whether there is one agree- ment or several. United States v. Crosby, 294 F.2d 928 (2d Cir. 1961); Green v. United States, 332 F.2d 788, 789 (5th Cir. 1964); United States v. American Honda Motor Co., 273 F. Supp. 810 (N.D. Ill. 1967). Varelli, supra, 407 F.2d at 746. Thus the trial court upon remand should provide jury instructions that will insure that the jury is aware of the alternatives of’ finding single or multiple conspiracies in the evidence presented by plaintiffs. The defendants raise several questions about the legal! sufficiency of plaintiffs’ conspiracy claims which must be discussed. First, defendants contend that in order to have an adequate claim for relief under section 1983, a plaintiff must allege and prove both a conspiracy and an actual deprivation of rights; mere proof of a conspiracy is insufficient to establish a section 1983 claim. This statement of the law is correct, see Lesser v. Braniff Atr- ways, Inc., 518 F.2d 538, 540 n. 2 (7th Cir. 1975), but we do not see how this affects the viability of plaintiffs’ claims in the instant case. Plaintiffs’ prima facie case offers a number of constitutional deprivations to accom- pany their conspiracy allegations; clearly, the evidence would support a finding of injury which would con- stitute deprivation of constitutional rights. Thus, this re- quirement of a section 1988 claim has been satisfied. The federal defendants also contend that section 1983 is inapplicable to them since its prohibitions are directed only against state actors. Yet when federal of- ficials are engaged in a conspiracy with state officials to deprive constitutional rights, the state officials provide the requisite state action to make the entire conspiracy actionable under section 19838. The Second Circuit has stated: “When the violation is the joint product of the ex- ercise of a State power and of a non-State power then the test under the Fourteenth Amendment and § 1983 is whether the state or its officials played a ‘significant’ role in the result.” Kletschka v. Driver, 411 F.2d 436, 449 (2d Cir. 1969) (éitation omitted.) Our recent decision in