New alleles become fixed owing to random drift of nearly neutral mutations or to positive selection of substantially advantageous mutations. After decades of debate, the fraction of fixations driven by selection remains uncertain. Within 9,390 genes, we analysed 28,196 codons at which rat and mouse differ from each other at two nucleotide sites and 1,982 codons with three differences. At codons where rat-mouse divergence involved two non-synonymous substitutions, both of them occurred in the same lineage, either rat or mouse, in 64% of cases; however, independent substitutions would occur in the same lineage with a probability of only 50%. All three non-synonymous substitutions occurred in the same lineage for 46% of codons, instead of the 25% expected. Furthermore, comparison of 12 pairs of prokaryotic genomes also shows clumping of multiple non-synonymous substitutions in the same lineage. This pattern cannot be explained by correlated mutation or episodes of relaxed negative selection, but instead indicates that positive selection acts at many sites of rapid, successive amino acid replacement.