The task of combining evolutionary migration models with stochastic utility theory is undertaken in a series of three interrelated papers. The present, first, paper deals with the evolution of migratory systems and its dynamics are drawn mainly from work by Haag and Weidlich. A migratory system is defined and then the foundations upon which the evolution of such a system is based are described, including an approximation due to Kurtz which allows the most probable state of the evolutionary model to be represented as a dynamical system. This paper closes with a discussion of disequilibrium, which is central in this series. Disequilibrium is related to the concept of a steady state, the existence of which is established for nonlinear migratory systems of the type discussed here.