Visco-elastic models are commonly used in modeling time dependent behavior of asphalts, polymers, and biomaterials (e.g., soft tissues). In order to ensure that these models are thermomechanically consistent, their stress-strain behavior has to be derived using a strain energy function. For a non-linear viscoelastic behavior, this appears to be a rather subtle problem: some quasi-linear viscoelastic energy formulations presented in the literature do not use the true energy functions for the stress-strain response attributed to these models, making their mechanical interpretation and validation of thermomechanical consistency difficult. This paper represents an attempt to propose an alternative framework, which would retain simplicity and convenience in numerical applications of the quasi-linear viscoelasticity, but would have a straightforward mechanical interpretation and guarantee the thermomechanical consistency. This is achieved by using a thermomechanical approach with internal kinematic variables, where both the energy and dissipation potentials have the same kind of non-linearity, leading to a general family of non-linear visco-elastic models. Within this context, a simple thermomechanically consistent non-linear hyperviscoelastic model with pressure dependent bulk stiffness is proposed, with an example modeling experimental data from laboratory tests on asphalts. (C) 2010 The Society of Rheology. [DOI: 10.1122/1.3378879]