The authors propose a nonlocal rate-type constitutive equation including the Maxwell’s terms as well as higher order strain gradients in the additional relaxation function. The corresponding model should account for micro-structural and non-equilibrium effects in phase transition. The model can be deduced from the thermodynamics of non-simple bodies with internal variables. The authors analyse the compatibility with the second law of thermodynamics in order to establish explicit sufficient conditions for the compatibility with the Clausius-Duhem inequality and with the balance equations. Additionally, it is shown that the model is a nonlocal Sokolovskii-Malvern type one. In the one-dimensional case, the authors obtain energy estimates, a free energy function, and a controlled strain-rate with non-rapidly varying strain. Further they study the influence of rate-dependent effects on the local behaviour of solutions for a second-order gradient viscoplastic model. The diagrams show the boundaries of equilibrium domains in the stress-strain and stress-second order gradient spaces, which allows to determine the critical wave lengths in instability and pattern formation ranges. The variation of wave numbers versus a modulus-dependent term and the admissible domains for real roots are shown in diagrams in the dynamic case.