Inverted cubic and isotropic phases have been observed in phospholipid and glycolipid systems. These phases exhibit characteristic morphologies in freeze-fracture electron micrographs, isotropic 31P-NMR resonances and (in some cases) cubic X-ray diffraction patterns. It is proposed here that these phases may form from the same intermediates that are involved in lamellar/inverted hexagonal (L alpha/HII) phase transitions, and that it is possible that these cubic and isotropic phases are metastable. According to a kinetic theory of L alpha/HII phase transitions, intermediates in such transitions can form structures known as interlamellar attachments (ILAs). It is shown that ILAs should form in large numbers during L alpha/HII transitions in systems like those reported to form inverted cubic or isotropic structures. ILAs cannot readily assemble into either the HII phase or well-ordered arrays of L alpha phase bilayers, and represent a kinetic trap for intermediates in L alpha/HII transitions (although it is possible that they are marginally more stable in a thermodynamic sense than the L alpha phase in a small temperature range below TH). It is also shown that arrays of ILAs should form metastable arrays with the same morphology and isotropic 31P-NMR resonances that are observed in isotropic and inverted cubic states. In particular, under some circumstances ILAs will assemble into a structure identical to the bicontinuous inverted cubic phase previously described in monoglycerides and very similar in morphology to structures observed in phospholipid systems. Finally, since isotropic and cubic states form from ILAs, which also can mediate fusion of unilamellar vesicles, unilamellar vesicles should fuse to at least some extent under the same conditions in which multilamellar samples of the same lipid form isotropic or inverted cubic states. This correlation has been observed.