A procedure has been developed for analyzing the evolution with time of the volume fraction crystallized and for calculating the kinetic parameters at non-isothermal reactions in materials involving formation and growth of nuclei. By means of this method, and considering the assumptions of extended volume and random nucleation, a general expression of the fraction crystallized has been obtained, as a function of time. In the quoted expression one considers that the crystal growth rate is anisotropic. In addition, the particular case of isotropic growth rate has been studied, and the obtained equation has been integrated for the important case of nucleation frequency and growth rate independent of time, resulting an expression that may be taken as a detailed specific case of the Johnson-Mehl-Avrami relation. The kinetic parameters have been deduced, fitting a theoretical function, obtained from the JMA model to the experimental data, temperature and volume fraction crystallized. A least-squares method has been used, bearing in mind the fact that, in most non-isothermal processes, the reaction rate constant exhibits an Arrhenian temperature dependence. Finally, the theoretical derivations of the kinetic parameters have been applied to the experimental data corresponding to a set of glassy alloys, quoted in the literature, thus obtaining mean values that agree very satisfactorily with the bibliographical data. This fact shows the reliability of the developed theoretical method.