Summary The simulation of the viscous behavior of some clays is of high importance in many geotechnical problems. The literature offers a vast amount of constitutive models able to simulate the rate dependence observed on these materials. Although most of these models are calibrated to very similar experimental observations and share similar definitions of material parameters, some discrepancies of their response have been detected, which are related to their mathematical formulations. In this work, the causes of these discrepancies are carefully studied. To that end, four different model families are analyzed, namely, nonstationary flow surface (NSFS) models, viscoplasticity with overstress function (OVP), viscoplasticity with Norton's power law (NVP), and visco‐hypoplasticity (VHP). For the sake of a fair comparison, single constitutive models using the same set of material parameters, and following other requirements, are developed for each model family. Numerical implementations of the four resulting models are performed. Their response at different tests are carefully analyzed through simulation examples and direct examination of their constitutive equations. The set includes some basic tests at isotropic stress states and others as responses envelopes, undrained creep rupture, and an oedometer test with loading, unloading‐reloading, creep, and relaxation. The article is concluded with some remarks about the observed discrepancies of these model families.