The population dynamics of nearly neutral mutations are studied using a single-site and a multisite model. In the latter model, the nucleotides in a sequence are completely linked and the selection schemes employed are additive, multiplicative, and additive with a threshold. Although the third selection scheme is very different from the first two, the three schemes produce identical results for a wide range of parameter values. Thus the present study provides a general theory for the population dynamics of nearly neutral mutations because the results can also be used to draw inferences about other selection schemes such as stabilizing selection and synergistic selection. It is shown that the number of slightly deleterious mutations accumulated in a sequence can be considerably larger under the multisite model than under the single-site model, particularly if the sequence is long or if the mutation rate per site is high. The results show that even a very slight selective difference between synonymous codons can produce a strong bias in codon usage. Three alternative explanations for the strong bias in codon usage in bacterial and yeast genes are considered. The implications of the present results for molecular evolution are discussed.