A theory introduced by Ronald Langacker is used to analyze the English modal auxiliary verb system. The theory synthesizes generative semantics and notions from cognitive psychology, and posits a close link between form and meaning and denies the existence of autonomous syntactic and semantic components in linguistic structure. The intent of the analysis is to: (1) create a framework for making sense of apparent inconsistencies between the forms of English modals and their meanings and uses, especially the relationship between the historical present (e.g., "may") and past (e.g., "might") tenses of the auxiliaries; and (2) to illustrate how semantically based theories of language structure can be of value to teachers of English as a second language (ESL) and language teachers in general in ways that purely syntactic theories can not. Four major points emerging from the analysis that might be useful to ESL teachers are summarized, and some possible classroom presentations of the information are suggested. (MSE)