A computer model of a tsetse population was developed to determine whether insecticide resistance could evolve as a result of current tsetse control programmes. Chemical analyses were also carried out which showed that Glossina morsitans morsitans Westw. can metabolise DDT to DDE, indicating a potential for insecticide resistance in this species. The model showed that a completely isolated tsetse population stands little chance of surviving attacks with insecticides repeated at short intervals. However, when sufficient time is allowed between applications, such a population may survive and evolution of resistance take place. Given a small amount of immigration, the evolution of resistance is retarded, but population extinction is prevented. The degree of resistance developed by a population also depends on the dominance relationship of a resistant gene with its wild-type allele and on the reproductive fitness of the mutant. It is suggested that control strategies are adopted which would minimise the risk of insecticide resistance becoming a problem in tsetse and that susceptibility studies are carried out both before spraying operations and on any residual population post-spraying.