The structural parameters of the hexagonal and lamellar phase of the dimethyldodecylamine oxide (DDAO)-water and the dimethyl-dodecylphosphine oxide (DDPO)-water systems have been determined using X-ray diffraction. In addition the relative vapour pressure of water in equilibrium with these phases was determined as a function of surfactant concentration and temperature. This allowed the determination of the swelling pressure in the lamellar phase. It was found that the swelling pressure was considerably higher in the DDAO-water system than in DDPO-water. For both surfactants, but most pronounced so for DDPO, the swelling pressure decreased with increasing temperature. The results obtained are discussed in the light of the ongoing debates about i) the relative importance of steric/protrusion forces and hydration forces between surfactant bilayers, and ii) the molecular origin of the temperature dependence of the interactions displayed in several non-ionic - water systems.