The rates of crystallization of five polymers, poly‐(ethylene oxide), poly‐(decamethylene adipate), and three poly‐(N,N′‐sebacoyl piperazine)'s differing in molecular weight, have been observed dilatometrically at various temperatures ranging from 5.5 to 24° below the respective melting pointsTm. The crystallization isotherms are remarkably reproducible, and the previous thermal history above the melting point is without effect provided that melting is completed before the crystallization experiment is begun. The crystallization isotherms display induction periods. The very large temperature coefficients observed are uniform throughout the crystallization process, i.e., isotherms at different temperatures are superimposable by rescaling the time. It is inferred from this and other evidence that steady‐state nucleation and growth occur simultaneously throughout the process. The results are satisfactorily interpreted by applying conventional nucleation theory and assuming that nuclei grow at rates proportional to their surface areas. The treatment resembles that applied to crystallization in metals. Spherical and disk‐shaped nuclei are considered, but the data do not discriminate between them. An extension of the theory accounts for the maximum commonly observed in the crystallization rate as the temperature is decreased below the range of the present measurements.