This paper aims at proving that, contrary to previous contributions to the subject, Hillsconception of the nonlinear self-consistent scheme, which has been applied in the past toelastoplasticity and to viscoplasticity, can still be adopted with success for elastoviscoplasticity.After a qualitative presentation of the main arguments for this statement, a new Hill-typeapproach is proposed for rate-dependent elastoplastic heterogeneous materials. The associatedlinearization procedure relies on an affine formulation instead of Hills incremental one and onthe use of the correspondence principle to solve the concentration problem; this problem isproved to reduce to a linear viscoelastic one with eigenstrain, i.e. to a linear thermoviscoelasticproblem. The full set of equations is reported for the case of the self-consistent scheme andillustrative applications are given for polycrystals: they are shown to be, as expected, alwayssofter than Kröner-type predictions and to take better into account the viscoelastic coupling andthe associated long range memory effect. In conclusion, the connection and differences betweenthe present approach and other ones already proposed for viscoplastic materials is emphasizedand the limits of Hills conception itself are acknowledged and discussed.