The general theory of phase transformation kinetics, derived independently by Kolmogorov, Johnson and Mehl, and Avrami (KJMA), has been used intensively by materials scientists to study various mechanisms of phase transformations in metals, polymers and glasses, especially in kinetic calculations of glass formation. The theory is certainly valid within the framework of its assumptions, and thus its violation in certain cases can be used to infer hidden details of the crystallization mechanisms of supercooled liquids. In this paper the applicability of the KJMA theory to glass crystallization is discussed for three transformation mechanisms : (i) volume crystallization of single crystals, (ii) volume crystallization of branched crystals, and (iii) surface crystallization, in the following silicate glasses : Na2O.2CaO.3SiO(2); Li2O.2SiO(2) and CaO.MgO.2SiO(2).