The determination of the chimpanzee genome sequence provides a means to study both structural and functional aspects of the evolution of the human genome. Here we compare humans and chimpanzees with respect to differences in expression levels and protein-coding sequences for genes active in brain, heart, liver, kidney, and testis. We find that the patterns of differences in gene expression and gene sequences are markedly similar. In particular, there is a gradation of selective constraints among the tissues so that the brain shows the least differences between the species whereas liver shows the most. Furthermore, expression levels as well as amino acid sequences of genes active in more tissues have diverged less between the species than have genes active in fewer tissues. In general, these patterns are consistent with a model of neutral evolution with negative selection. However, for X-chromosomal genes expressed in testis, patterns suggestive of positive selection on sequence changes as well as expression changes are seen. Furthermore, although genes expressed in the brain have changed less than have genes expressed in other tissues, in agreement with previous work we find that genes active in brain have accumulated more changes on the human than on the chimpanzee lineage.