Two viscoelastic constitutive relations in differential form are further developed here to include material nonlinearity and distinction between loading and unloading regimes, which is a characteristic of polymers. The effects of hydrostatic pressure and anisotropy in tension and compression on the deformation response of polymers are accounted for through the definition of a pressure-dependent equivalent stress. In the uniaxial stress state, these constitutive relations reduce to the two well-known mechanical analogue representations: "Kelvin-Voigt-type" and "Maxwell-type" rheological models. The predictive capabilities of these constitutive relations are then assessed against a wide range of experimental results, which include both uniaxial and biaxial stress states subjected to quasi-static and cyclic-loading conditions. The predictions of both models are found to be in good agreement with the test data.