The Stoics extensively discussed logical paradoxes and fallacies, both of which they would call sophisms (σοφίσματα). They wrote numerous books on the paradoxes of the Liar and the Sorites, which today – again – are the subject of extensive research; they investigated a number of paradoxes and fallacies that are based on puzzles connected with demonstratives, identity, presuppositions and ambiguities, and there are still many questions unanswered about their treatment of each of these. In this paper I take up the Stoic treatment of sophisms or fallacies which contain ambiguities, more precisely which contain an ambiguous word which is responsible for there being a fallacy. In modern terms, these are lexical, as opposed to grammatical or structural, ambiguities, and this kind of fallacy is often called ‘fallacy of equivocation’, although we cannot assume that the Stoic understanding of such ambiguities fully coincides with any modern ones. The Peripatetics called such fallacies fallacies of homonymy, and the Stoics are likely to have called them fallacies of homonymy in single words. The Stoic discussion of this type of fallacies has been written upon with fruitful results by several scholars, but the precise nature of the Stoic view is still a matter of debate. In this paper, I try to sort out the difficulties for an interpretation of the Stoic treatment of such fallacies based on lexical ambiguities, compare it with Aristotle's treatment of this type of sophisms, and explore what we can learn from it about Stoic theory of logic and language.