Time-resolved-X-ray diffraction was employed to monitor transitions, induced by pressure jumps, between inverse lyotropic liquid crystalline phases of the mixed lipid system lauric acid/dilauroylphosphatidylcholine (2:1 molar ratio) in water. We studied transitions between the gyroid, Q(II)(G), and the double diamond, Q(II)(D), inverse bicontinuous cubic phases and between Q(II)(D) and the inverse hexagonal, H-II, phase at a fixed water composition of 50 wt %. The transition Q(II)(G) --> Q(II)(D) occurred within the 0.5 s time resolution of our X-ray measurements; This transition occurs without any change in water content within the mesophase but with a small change in the total topology. The transition Q(II)(D)-->(Q(II)(D)+H-II+excess water) was observed at 59.3, 62.8, and 66.9 degrees C, The process appeared to follow first-order kinetics, with rate constants of 0.11, 0.17, and 0.26 S-1, respectively. The reverse transition occurred much more quickly, being completed in <1 s. In both cases, intermediate structures were observed, including the appearance of the inverse bicontinuous cubic phase based on Schwarz's P minimal surface, Q(II)(P). We found that the latter intermediate had, to first order, the same curvature elastic energy as the Q(II)(D) phase but a greater water content. Building on earlier work (Erbes, J.; Winter, R.; Rapp, G, Ber. Bunsen-Ges. Phys. Chem. Chem. Phys. 1996, 100, 1723-1722), we consider the rate to depend on the difference between the final pressure and the pressure at the phase transition boundary and suggest that this can explain both the temperature dependence of the transition Q(II)(D)-->(Q(II)(D)+H-II+excess water) and the higher rate of the reverse process.