Using the pressure-jump relaxation technique in combination with synchrotron X-ray diffraction we have investigated the rate and mechanism of phase transformations of mesophases of the lecithin/fatty acid mixtures dimyristoylphosphatidylcholine/myristic acid (DMPC/MA) and dipalmitoylphosphatidylcholine/palmitic acid (DPPC/PA) in the molar ratio 1:2. The investigations have been made as a function of the pressure-jump amplitude and at two different levels of hydration, 50 and 75 wt% H2O. For the investigation of the structure of the lipid systems at elevated pressures as well as for the study of the kinetics of lipid phase transitions using the pressure-jump technique, we built a high pressure X-ray cell suitable for studies up to pressures of 2 kbar at temperatures ranging up to 140 degrees C. In the first part of the paper, the temperature and pressure dependent structure and equilibrium phase behaviour of the two lecithin/fatty acid mixtures is discussed. In equilibrium, the chain melting transition of both mixtures occurs without forming a lamellar liquid-crystalline L(alpha) phase. In DMPC/MA (1:2) dispersions the phase sequence is L(c)(com)/L(c)-->H-II/Q(II)(P)/Q(II)(D)-->H-II, in DPPC/PA (1:2) L(c)(com)/L(c)-->L(beta)-->H-II with increasing temperature or decreasing pressure, respectively. A temperature-pressure phase diagram has been established in the temperature range from 0-100 degrees C at pressures from ambient up to 1500 bar for both systems. Pressure-jumps within the inverted hexagonal/Q(II)(P) cubic phase coexisting region of DMPC/MA (1:2) lead to a slight change of the composition of the mixture, and the structural relaxation process of the lattices proceeds in several steps. The rate-determining part of the structural relaxation process is probably due to the restricted diffusion of water in and into the lattices and the relaxation of the hexagonal and cubic structures are found to be coupled to each other. Equilibrium values of the lattice constants are reached after about 30 s. Formation of further cubic lattices is possible, depending on the level of hydration. Experiments on the rate of the L(beta)-->H-II/Q(II)(P) chain melting transition of DMPC/MA (1:2) exhibit the occurence of a long-lived intermediate L(alpha) phase, which is not observed under equilibrium conditions. The H-II lattice starts to develop within the lime-resolution of this experiment, i.e. within the first 200 ms. First Bragg reflections of the cubic phase appear about 100 s after the pressure-jump. Equilibrium values of the lattice constants are not reached before 30 min. The pressure-jump amplitude has been found to have a significant influence on the kinetics of the phase transformation, the mechanism remaining. The increase of the pressure-jump amplitude leads to a faster decay of the L(beta) phase and the more rapid formation of the H-II phase. The L(beta)-->H-II transition of DPPC/PA (1:2) dispersion follows a simpler kinetics. No intermediate L(alpha) phase is found. The transition is complete about 25 s after a pressure-jump from 520 to 200 bar at 71 degrees C, and it seems to be a simple two-state process to within the sensitivity limit of these experiments.