Language acquisition and processing are governed by genetic constraints. A crucial unresolved question is how far these genetic constraints have coevolved with language, perhaps resulting in a highly specialized and species-specific language ''module,'' and how much language acquisition and processing redeploy preexisting cognitive machinery. In the present work, we explored the circumstances under which genes encoding language-specific properties could have coevolved with language itself. We present a theoretical model, implemented in computer simulations, of key aspects of the interaction of genes and language. Our results show that genes for language could have coevolved only with highly stable aspects of the linguistic environment; a rapidly changing linguistic environment does not provide a stable target for natural selection. Thus, a biological endowment could not coevolve with properties of language that began as learned cultural conventions, because cultural conventions change much more rapidly than genes. We argue that this rules out the possibility that arbitrary properties of language, including abstract syntactic principles governing phrase structure, case marking, and agreement, have been built into a ''language module'' by natural selection. The genetic basis of human language acquisition and processing did not coevolve with language, but primarily predates the emergence of language. As suggested by Darwin, the fit between language and its underlying mechanisms arose because language has evolved to fit the human brain, rather than the reverse.Baldwin effect ͉ coevolution ͉ cultural evolution ͉ language acquisition