Two sorts of inverted micellar structures have previously been proposed to explain morphological and 31P-NMR observations of bilayer systems. These structures only form in systems with components that can adopt the inverse hexagonal (HII) phase. LIP (lipidic particles) are intrabilayer structures, whereas IMI (inverted micellar intermediates) are structures that form between apposed bilayers. Here, we calculate the formation rates and half-lives of these structures to determine which (or if either) of these proposed structures is a likely explanation of the data. Calculations for the egg phosphatidylethanolamine and the Ca+-cardiolipin systems show that IMI form orders of magnitude faster than LIP, which should form slowly, if at all. This result is probably true in general, and indicates that "lipidic particle" electron micrograph images probably represent interbilayer structures, as some have previously proposed. It is shown here that IMI are likely intermediates in the lamellar----HII phase transitions and in the process of membrane fusion in some systems. The calculated formation rates, half-lives, and vesicle-vesicle fusion rates are in agreement with this observation.