This paper is devoted to a self-consistent derivation of the overall behaviour of multiphase materials from those of the constituent phases when these phases obey rate-dependent elastic-plastic constitutive equations. We have already proposed a solution to this still unsolved problem in the case of quite simple constitutive equations. In this paper, the formulation is extended to more general ones, including internal parameters: such a description can be specified for the case of rate-dependent elastic-plastic polycrystals and the classically associated constitutive equations. It is shown that the merits of the proposed formulation are saved at the expense of limited complication. A simple application is given as an illustration of the tractability of the method.