The general distinction between morphology and syntax is widely taken for granted, but it crucially depends on a cross-linguistically valid concept of ‘(morphosyntactic) word’. I show that there are no good criteria for defining such a concept. I examine ten criteria in some detail (potential pauses, free occurrence, mobility, uninterruptibility, non-selectivity, non-coordinatability, anaphoric islandhood, nonextractability, morphophonological idiosyncrasies, and deviations from bi-uniqueness), and I show that none of them is necessary and sufficient on its own, and no combination of them gives a definition of ‘word’ that accords with linguists’ orthographic practice. ‘Word’ can be defined as a language-specific concept, but this is not relevant to the general question pursued here. ‘Word’ can be defined as a fuzzy concept, but this is theoretically meaningful only if the continuum between affixes and words, or words and phrases, shows some clustering, for which there is no systematic evidence at present. Thus, I conclude that we do not currently have a good basis for dividing the domain of morphosyntax into morphology and syntax, and that linguists should be very careful with general claims that make crucial reference to a cross-linguistic ‘word’ notion.