The paper proposes a stress-driven integration strategy for Perzyna-type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity-like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m-AGC tangent operator. This operator is combined with the stress-prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra-step iterations (in physical viscoplasticity), or to a variable time-step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero-thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed.