Crystallization of polyethylene terephthalate and i-polypropylene in nonisothermal conditions is studied by means of differential scanning calorimetry. Measurements, carried out at several constant cooling rates, are interpreted in terms of a new theory(1,2) that takes into account effects related to a transient, nonsteady-state course of the process as well as athermal nucleation, which may occur under such circumstances. This article gives preliminary results based on analysis of final crystallinity reached at the end of cooling. Results indicate that the classical isokinetic approach is not adequate to describe crystallization kinetics at high cooling rates. A parameter quantizing the magnitude of deviations from isokinetic law is evaluated.