In cognitive semantics, metaphors are cross-domain mappings in the conceptual system. Thus the notion of domain plays a crucial role in the theory. However, domain is never defined, but taken for granted. Using data from language acquisition, production, and comprehension, the cognitive status of the notion of domain is questioned, and it is demonstrated that both linguistic and nonlinguistic evidence indicate that space and time are cognitively linked in a way that is incompatible with the claim that space is mapped onto time in the development of grammatical temporal markers. (Copyright 1996, Sociological Abstracts, Inc., all rights reserved.) (LLBA 1996, vol. 30, n. 2)