The secondary crystallization and its influence on the glass transition are studied as a function of crystallization temperature and time by differential scanning calorimetry for PEEK. The multiple melting behavior resulting from isothermal annealing from the glass or crystallization from the melt is discussed in the context of models considering either a melting-recrystallization-remelting process or a bimodal population of primary and secondary crystals. The heating rate dependence of the multiple melting behavior indicates that reorganization of primary crystals occurs during heating for samples annealed from the glassy state but is insignificant for those crystallized from the melt. For either mode of crystallization, the high- and low-temperature endothermic regions are associated with the melting of primary and secondary crystals, respectively. Investigations of the low endotherm transition temperature and heat of fusion as a function of crystallization time and temperature lead to the following conclusions: the melting temperature of secondary crystals increases linearly with the logarithm of secondary crystallization time at a rate, B(T), increasing linearly with decreasing temperature; the Avrami exponent, which characterizes the initial stage of secondary crystallization, is constant below ca. 310 degrees C (n = 1/2) but increases gradually with temperature above 310 degrees C; the late stage of secondary crystallization is characterized by a linear increase in crystallinity with logarithm of time. Studies of the evolution of the glass transition after secondary crystallization indicate that the calorimetric T-g increases linearly with the logarithm of time at a rate, b(T), increasing with decreasing temperature. Finally, a qualitative model of polymer crystallization of semiflexible polymer chains is proposed. This model considers the effect of structural constraints (chain stiffness) on the nature of the amorphous phase after primary crystallization and the effect of topological constraints (pinning of amorphous chains) on the secondary crystallization behavior.