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For a class of stochastic delay evolution equations driven by cylindrical$Q$-Wiener process, we study the Pontryagin's maximum principle for thestochastic recursive optimal control problem. The delays are given as movingaverages with respect to general finite measures and appear in all thecoefficients of the control system. In particular, the final cost can containthe state delay. To derive the main result, we introduce a new form ofanticipated backward stochastic evolution equations with terminals acting on aninterval as the adjoint equations of the delayed state equations and deploy aproper dual analysis between them. Under certain convex assumption on thecoefficient function and the Hamiltonian, we also show sufficiency of themaximum principle.

Maximum principle for recursive optimal control problem of stochastic delay evolution equations