The activation energy, E, of nonisothermal crystallization of polymer melts has been frequently evaluated by the Kissinger equation with positive rates of temperature variation, beta. It is demonstrated that reversing the sign for beta is a mathematically invalid procedure that generally invalidates the Kissinger method. As an alternative we propose the advanced isoconversional method that can be used for evaluating the effective activation energy of nonisothermal crystallization of the polymer melts. The application of this method to calorimetric data on crystallization of poly(ethylene terephthalate) (PET) yields an activation energy that increases with the extent of crystallization from -270 to +20 kJ mol(-1). It is demonstrated that this variation is consistent with data on isothermal crystallization of the PET melts and can be interpreted in terms of the accepted crystallization models.