Abstract The research topics involving adsorption kinetics of chemical substances on clays and related materials include hundreds of papers over the last decades. In many of them, it is concluded that the adsorption is governed by the so-called pseudo-second order (PSO) mechanism. These conclusions mostly come from regression analysis of adsorption data using the simplified linearized form of the model. The in-depth analysis presented in this paper shows the unsuitability of the linearized function to evaluate the goodness of the PSO model for adsorption data. This paper presents more accurate ways of testing adsorption data using original non-linear models. The results have a significant impact on the reassessment of the interpretations published in earlier studies aimed at adsorption kinetics for the systems based on clays, as well as other adsorbents and materials.