A model of the energetics of lipid assemblies (Siegel. 1993. Biophys. J. 65:2124-2140) is used to predict the relative free energy of intermediates in the transitions between lamellar (Lalpha) inverted hexagonal (HII), and inverted cubic (QII) phases. The model was previously used to generate the modified stalk theory of membrane fusion. The modified stalk theory proposes that the lowest energy structures to form between apposed membranes are the stalk and the transmonolayer contact (TMC), respectively. The first steps in the Lalpha/HII and Lalpha/QII phase transitions are also intermembrane events: bilayers of the Lalpha phase must interact to form new topologies during these transitions. Hence the intermediates in these phase transitions should be similar to the intermediates in the modified stalk mechanism of fusion. The calculations here show that stalks and TMCs can mediate transitions between the Lalpha, QII, and HII phases. These predictions are supported by studies of the mechanism of these transitions via time-resolved cryoelectron microscopy (. Biophys. J. 66:402-414; Siegel and Epand. 1997. Biophys. J. 73:3089-3111), whereas the predictions of previously proposed transition mechanisms are not. The model also predicts that QII phases should be thermodynamically stable in all thermotropic lipid systems. The profound hysteresis in Lalpha/QII transitions in some phospholipid systems may be due to lipid composition-dependent effects other than differences in lipid spontaneous curvature. The relevant composition-dependent properties are the Gaussian curvature modulus and the membrane rupture tension, which could change the stability of TMCs. TMC stability also influences the rate of membrane fusion of apposed bilayers, so these two properties may also affect the fusion rate in model membrane and biomembrane systems. One way proteins catalyze membrane fusion may be by making local changes in these lipid properties. Finally, although the model identifies stalks and TMCs as the lowest energy intermembrane intermediates in fusion and lamellar/inverted phase transitions, the stalk and TMC energies calculated by the present model are still large. This suggests that there are deficiencies in the current model for intermediates or intermediate energies. The possible nature of these deficiencies is discussed.