Specific sets of brain-expressed genes, such as aerobic energy metabolism genes, evolved adaptively in the ancestry of humans and may have evolved adaptively in the ancestry of other large-brained mammals. The recent addition of genomes from two afrotherians (elephant and tenrec) to the expanding set of publically available sequenced mammalian genomes provided an opportunity to test this hypothesis. Elephants resemble humans by having large brains and long life spans; tenrecs, in contrast, have small brains and short life spans. Thus, we investigated whether the phylogenomic patterns of adaptive evolution are more similar between elephant and human than between either elephant and tenrec lineages or human and mouse lineages, and whether aerobic energy metabolism genes are especially well represented in the elephant and human patterns. Our analyses encompassed approximately 6000 genes in each of these lineages with each gene yielding extensive coding sequence matches in interordinal comparisons. Each gene's nonsynonymous and synonymous nucleotide substitution rates and dN/dS ratios were determined. Then, from gene ontology information on genes with the higher dN/dS ratios, we identified the more prevalent sets of genes that belong to specific functional categories and that evolved adaptively. Elephant and human lineages showed much slower nucleotide substitution rates than tenrec and mouse lineages but more adaptively evolved genes. In correlation with absolute brain size and brain oxygen consumption being largest in elephants and next largest in humans, adaptively evolved aerobic energy metabolism genes were most evident in the elephant lineage and next most evident in the human lineage.