The kinetics of a model for the primer‐dependent, polynucleotide phosphorylase‐catalyzed synthesis of oligo‐ and polynucleotides is developed. Numerical solutions are presented which correspond to a wide variety of possible reaction conditions. The model seems capable of explaining the types of behavior which have been experimentally observed for polynucleotide phosphorylase reactions. The most unusual of these is the presence of a transient intermediate of high molecular weight polynucleotide chains which is subsequently degraded to an equilibrium mixture of short oligonucleotides. Methods of estimating the time of occurrence and maximum size of the polymer are discussed. Analytical solutions are developed for the concentrations of free enzyme and unreacted nucleoside diphosphate. In conjunction with equilibrium data these may permit the rate constants required by the model to be determined. Copyright © 1968 John Wiley & Sons, Inc.