In general, there have been two main approaches for ruling out such sequences of modals: the phrase-structure (P-S) rule approach advocated by proponents of the Aux analysis which relies on P-S rules containing only one modal per surface clause (e.g., Chomsky 1957; Akmajian, Steele and Wasow 1979); and the subcategorization approach, proposed by advocates of the Main Verb analysis, which assumes that modals are finite forms and are subcategorized for stem forms (e.g., Baker 1981; Gazdar, Pullum and Sag 1982). One problem that both types of analyses face is that there are large numbers of English speakers, most notably in the South Midland and Southern United States, who regularly use double modals (DM's), as in (2)-(8).2