In this paper we describe the nature and importance of processive enzymatic reactions in biological processes. A model is set up to describe the processive synthetic process in DNA replication, and experiments are presented to define and test the model, using the components of the T4 phage-coded five-protein (in vitro) DNA replication system of Alberts. Nossal and coworkers. These experiments are performed either with a homogeneous oligo dT-poly dA primer-template system, or with a natural primer-template system using phage M13 DNA. The results are used to define some molecular aspects of the microscopic "processivity cycle".