We have investigated a section through the composition-temperature pha
se prism of a ternary nonionic surfactant-water-oil system defined by
a constant surfactant to water ratio. The structural sequence normal c
ylinders-multiply connected bilayer-planar bilayer-reverse monolayer s
tructure is obtained when increasing the temperature. This sequence co
rresponds to a gradual reversal of the mean curvature of the polar-apo
lar interface as the temperature is increased as has been observed pre
viously in the corresponding microemulsion systems. The cylinders can
incorporate (swell with) moderate amounts of oil. In addition to the b
icontinuous cubic phase present in the binary water-surfactant system
the ternary system contains a bicontinuous cubic phase with simultaneo
usly high contents of water and oil. Upon dilution with oil, this phas
e undergoes an order-disorder transition to a liquid ''sponge phase' (
L4) retaining the multiply connected bilayer structure. A lamellar pha
se swells with large amounts of oil. From the variation of the periodi
city with oil content we obtain the solubility of the nonionic surfact
ant in the oil.