  This paper deals with the existence and uniqueness of ($\mu$-pseudo) almost
periodic mild solution to some evolution equations with Stepanov ($\mu$-pseudo)
almost periodic coefficients, in both determinist and stochastic cases. After
revisiting some known concepts and properties of Stepanov ($\mu$-pseudo) almost
periodicity in complete metric space, we consider a semilinear stochastic
evolution equation on a Hilbert separable space with Stepanov ($\mu$-pseudo)
almost periodic coefficients. We show existence and uniqueness of the mild
solution which is ($\mu$-pseudo) almost periodic in 2-distribution. We also
generalize a result by Andres and Pennequin, according to which there is no
purely Stepanov almost periodic solutions to differential equations with
Stepanov almost periodic coefficients.
