In detecting natural selection operating at the amino acid sequence level by comparing the rates of synonymous (r(S)) and nonsynonymous (r(N)) substitutions, the rates of synonymous and nonsynonymous mutations are assumed to be approximately the same. In reality, however, these rates may not be the same if different proportions of synonymous and nonsynonymous sites overlap with CpG dinucleotides, which are known to be hypermutable in some organisms. Here, we develop the evolutionary pathway methods for comparing r(S) and r(N) at multiple codon sites (all-sites analysis) and at single codon sites (single-site analysis) that take into account the hypermutability at CpG dinucleotides in estimating the number of synonymous substitutions per synonymous site (d(S)) and nonsynonymous substitutions per nonsynonymous site (d(N)). Computer simulations show that the direction and magnitude of the bias in the estimation of d(N)/d(S) caused by the hypermutability of CpGs are determined by both the number of CpGs and the relative proportions of synonymous and nonsynonymous sites overlapping with CpGs. This bias is greatly reduced when using the methods we propose to account for the hypermutability of CpG dinucleotides. In an all-sites analysis of protamine 1 genes from primates, d(N)/d(S) > 1 was observed for many pairs if the hypermutability was ignored. However, d(N)/d(S) becomes <or=1 for most of these pairs when the CpG sites are assumed to be hypermutable. Therefore, statistical indications of positive selection in some sequences or individual codons may be caused by mutation rate differences in synonymous and nonsynonymous sites.