A Mori-Tanaka homogenization scheme based on the ``translated fields'' approach is extended to elasto-viscoplastic composites with non-linear viscoplasticity described by a first-order ``affine''-type linearization. This extension leads to a new theoretical interaction law between mechanical average phase fields and overall ones. This interaction law contains the coupling between elastic- and viscoplastic- mechanical interactions and phase stress histories. In order to study and discuss the validity of the present approach, the results are reported for two-phase composites and are compared to other approaches.