A model is developed to explain the following experimental observations: oligomers of the alternating DNA copolymer dAT serve as templates for the enzymatic synthesis of macromolecular dAT; the rate of polymer synthesis with a template oligomer of given length increases to a maximum and then decreases as the temperature increases; the temperature for the maximum rate of synthesis increases with the length of the template. These observations were interpreted in terms of the repeated “slipping” of the oligomer along the product strand to expose template sites. This communication extends this idea. We suppose that the rate‐limiting step in the polymerization is either the attachment of the substrate to the exposed template site or the synthesis of the phosphodiester bond. Then the rate of synthesis is proportional to the equilibrium concentration either of exposed template sites or of template sites occupied by substrate molecules. These concentrations are evaluated in terms of a simple theory of the helix–coil transition. The model qualitatively reproduces the dependence of the rate of synthesis on template length and temperature and predicts rates of synthesis in approximate agreement with experiment.