In this paper a stopping criterion for a particular class of evolutionary algorithms is devised. First, a model of a generic evolutionary algorithm using iterated random maps is presented. The model allows the exploration of a connection between coupling from the past, and a stopping criterion for evolutionary algorithms. Accordingly, a method to stop a generic evolutionary algorithm is proposed. Some computational experiments are carried out to test the stopping criterion, using a modified version of coupling from the past. Empirical evidence is shown to support the suitability of the criterion.