A theoretical method is derived for the progress of a nucleation and growth-controlled reaction during heating at a constant rate. The kinetic parameters have been obtained assuming that the reaction rate constant is a time function through its Arrhenian temperature dependence. Besides, it has been shown that the different models, used in the literature for analyzing the glass-crystal transformation, are particular cases of the general expression deduced for the actual volume fraction transformed. The model is applied to the DSC data of crystallization kinetics of the Ge0.18Sb0.23Se0.59 glassy alloy, thus obtaining values for the kinetic parameters that agree satisfactorily with the calculated results by the Austin-Rickett kinetic equation, under non-isothermal regime. This fact shows the reliability of the theoretical method developed. (c) 2005 Elsevier B.V. All rights reserved.