Mechanical behavior of double-network (DN) gels with covalent and non-covalent bonds under multi-cycle loading depends strongly on time, strain rate and deformation program. A model is developed for the viscoelastic and viscoplastic responses of a polymer network with permanent and temporary junctions. Viscoelasticity is modeled as breakage and reformation of temporary bonds driven by thermal fluctuations. Viscoplasticity is treated as sliding of permanent junctions with respect to their initial positions in the network. Slippage occurs when a junction becomes unbalanced due to transition of a chain linked by this junction from its active state into the dangling state. Analysis of observations in tensile tests with various strain rates, relaxation tests, loading-unloading tests, and multi-cycle tests with various deformation programs on a series of DN gels shows that the experimental stress-strain diagrams are described correctly by the governing equations, material parameters evolve consistently with experimental conditions, and predictions of the model are in quantitative (where sufficient data are provided) and qualitative agreement with experimental data. In particular, numerical simulation demonstrates the ability of the model to describe the Mullins effect in DN gels. (C) 2018 Elsevier Ltd. All rights reserved.