The molecular clock hypothesis states that protein-coding genes evolve at an approximately constant rate. However, this is only expected to be true as long as the function and the tertiary structure of the molecule remain unaltered. An important implication of this statement is that significant deviations in the rate of evolution of a gene with respect to the species clock are likely to reflect functional and/or structural alterations. Here, we present a method to identify such deviations and apply it to a data set of 2,929 high-quality coding sequence alignments corresponding to one-to-one orthologous genes from six mammalian species--human, macaque, mouse, rat, cow, and dog. Deviated branches are defined as those that present significant alterations in both the rate of nonsynonymous substitutions (dN) and the selective pressure (dN/dS). Strikingly, we find that as many as 24.5% of the genes show branch-specific deviations in dN and dN/dS, though this is a relatively well-conserved set of genes. Around half of these genes show branch-specific acceleration of evolutionary rates. Positive selection (PS) tests based on divergence data only identify 17.7% of the accelerated branches. Failure to identify PS in accelerated branches with an excess of radical amino acid replacements suggests that these tests are conservative. Interestingly, genes with accelerated branches are significantly enriched in neural proteins, indicating that this type of protein might play a more important role than previously thought in species diversification, although they are generally not detected by PS tests. We discuss in detail several examples of genes that show lineage-specific evolutionary rate acceleration and are involved in synaptic transmission, chemosensory perception, and ubiquitination.