This paper analyses the effects of selection against deleterious alleles maintained by mutation ('background selection') on rates of evolution and levels of genetic diversity at weakly selected, completely linked, loci. General formulae are derived for the expected rates of gene substitution and genetic diversity, relative to the neutral case, as a function of selection and dominance coefficients at the loci in question, and of the frequency of gametes that are free of deleterious mutations with respect to the loci responsible for background selection. As in the neutral case, most effects of background selection can be predicted by considering the effective size of the population to be multiplied by the frequency of mutation-free gametes. Levels of genetic diversity can be sharply reduced by background selection, with the result that values for sites under selection approach those for neutral variants subject to the same regime of background selection. Rates of fixation of slightly deleterious mutations are increased by background selection, and rates of fixation of advantageous mutations are reduced. The properties of sex-linked and autosomal loci in random-mating populations are compared, and the effects of background selection on asexual and self-fertilizing populations are considered. The implications of these results for the interpretation of studies of molecular evolution and variation are discussed.