ABSTRACT Gene frequencies in populations of haploid, asexual organisms are described by linear recurrence equations. Several models in which the mutation rate is controlled by one locus and the fitness is controlled at one or more other loci are developed. It is shown that good approximations can be introduced to give explicit solutions for the course of selection in these models. It is shown that a strong non-equilibrium selection for mutator genes is possible even when the presence of such a gene decreases the fitness of an individual. Experiments that corroborate these conclusions are discussed along with the effects of population size that determine the applicability of these results to natural populations.