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In this paper, we aim to develop the averaging principle for a slow-fastsystem of stochastic reaction-diffusion equations driven by Poisson randommeasures. The coefficients of the equation are assumed to be functions of time,and some of them are periodic or almost periodic. Therefore, the Poisson termneeds to be processed, and a new averaged equation needs to be given. For thisreason, the existence of time-dependent evolution family of measures associatedwith the fast equation is studied, and proved that it is almost periodic. Next,according to the characteristics of almost periodic functions, the averagedcoefficient is defined by the evolution family of measures, and the averagedequation is given. Finally, the validity of the averaging principle is verifiedby using the Khasminskii method.

Averaging principles for non-autonomous two-time-scale stochastic reaction-diffusion equations with jump