A thermodynamically consistent rate-type viscoelastic-viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time-dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one-dimensional rheo-logical model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub-components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time-dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time-dependent stress-strain responses of the PC can be reasonably predicted by the proposed model. (C) 2016 Society of Plastics Engineers