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Although it has been hypothesized for thirty years that many human adaptations are likely to be due to changes in gene regulation, almost nothing is known about the modes of natural selection acting on regulation in primates. Here we identify a set of genes for which expression is evolving under natural selection. We use a new multi-species complementary DNA array to compare steady-state messenger RNA levels in liver tissues within and between humans, chimpanzees, orangutans and rhesus macaques. Using estimates from a linear mixed model, we identify a set of genes for which expression levels have remained constant across the entire phylogeny (∼70 million years), and are therefore likely to be under stabilizing selection. Among the top candidates are five genes with expression levels that have previously been shown to be altered in liver carcinoma. We also find a number of genes with similar …