Thermal analysis methods are widely used to study crystallization kinetics in amorphous solids. The experimental data is frequently interpreted in terms of the Johnson-Mehl-Avrami (JMA) nucleation-growth model. This paper discusses the limits of such an approach. A simple and convenient method is proposed to verify the applicability of the JMA model as well as the basic assumptions of kinetic analysis. It is shown that the two parameter autocatalytic model includes the JMA model and that is a plausible description of the crystallization kinetics. The main advantage of this model is its flexibility in describing quantitatively the kinetics of complex crystallization processes. The experimental data for crystallization of a chalcogenide glass and zirconia gel analyzed in this paper clearly demonstrate the rather complex nature of these processes. As a consequence, it is very difficult to explore the real mechanism of the crystallization unless some complementary studies are made.