Constitutive equations are derived for the time- and rate-dependent response of double-network gels under three-dimensional deformation with finite strains accompanied by swelling. The polymer network of a gel involves permanent and transient components. Chains in the permanent network are bridged by covalent cross-links, while chains in the transient network are connected by temporary junctions that break and restore under loading. The model is applied to the analysis of tensile cyclic tests and relaxation tests on fully swollen specimens and constrained water uptake tests on as-prepared samples. Good agreement is demonstrated between experimental data and results of simulation.