A procedure has been developed to obtain an evolution equation with the temperature for the actual transformed volume fraction under non-isothermal regime, to calculate the kinetic parameters and to analyze the glass-crystal transformation mechanisms in solid systems where a large number of nuclei already exists and no other new nuclei are formed during the thermal treatment. In this case,it is assumed that the nuclei only grow, "site saturation", during the thermal process. Once an extended volume of transformed material has been defined and spatially random transformed regions have been assumed, a general expression of the extended volume fraction has been obtained as a function of the temperature. Considering the mutual interference of regions which grow from separate nuclei (impingement effect) and from the quoted expression, the actual transformed volume fraction has been deduced. The kinetic parameters have been obtained, by assuming that the reaction rate constant is a time function through its Arrhenian temperature dependence. The developed theoretical method has been applied to the crystallization kinetics of the Ag0.16As0.46Se0.38 glassy alloy as-quenched and previously reheated. In accordance with the corresponding results, it is possible to establish that in the considered alloy the nuclei were dominant before the thermal treatment, and because of it the reheating does not change in a considerable way the number of the pre-existing nuclei in the material, which is a case of "site saturation". The comparison of the quoted results with the values obtained by means of Matusita method confirms the reliability of the theoretical method developed (TMD). Moreover, the obtained values for the kinetic parameters coincide in a satisfactory way with the results calculated by means of the Austin-Rickett (AR) equation under non-isothermal regime. Besides, the experimental curve of the transformed fraction shows a better agreement with the theoretical curves of the developed method and of the Austin-Rickett model than with the corresponding curve of the Avrami model. Accordingly. it seems appropriate to choose the Austin-Rickett equation in order to describe the crystallization mechanism of the above-mentioned glassy alloy. (C) 2008 Elsevier B.V. All rights reserved.