For the case of weak selection, random assortment of gametes, and density-independent population regulation, we here establish the conditions under which an allele will spread in a population, with particular reference to the life-history effects of the allele, its level of dominance, and sex differences in its effects. Our treatment is simpler than that of Charlesworth (1980), but the results are essentially the same. We show that two quantities govern the selective dynamics of a two-allele single-locus system; these are level of dominance, and the difference between the per copy rates of increase of the alleles in homozygous populations. Our main conclusion is that the eventual outcome of evolution is unaffected by an allele's level of dominance, or sex differences in its effects, provided there is no overdominance. However, speed of progress to fixation is, of course, affected by these factors, and equations are derived to show how level of dominance affects speed of progress to fixation. When a dominant allele only affects the life history of one sex, its rate of spread is half that if both sexes are affected. The relationship between actual and intrinsic rates of increase is discussed and formulae are given showing the relationship for the case of weak selection.