The solubilization of a fluorocarbon oil in a nonionic fluorinated surfactant/water system is investigated by small-angle X-ray scattering to understand its role in the phase transitions between liquid crystals and to compare hydrogenated and fluorinated systems. The analysis of the phase behavior investigated between 5 and 40 degreesC shows the disappearance of the sponge phase even at low oil fractions whereas the lamellar and cubic phases are preserved and the hexagonal phase appears at high oil fractions due to the vanishing of the physical frustration of the curvature. The rate of oil incorporation is a function of both water-to-surfactant ratio and temperature, especially in the lamellar and cubic phases. Perfluorodecalin is mainly incorporated as a free film and induces a strong surfactant chain ordering in the hexagonal phase. In addition to to the lamellar/cubic transition previously pointed out in the binary system, the incorporation of oil induces new epitaxial relationships between the hexagonal phase and the two cubic structures of space groups Ia3d and Pn3m. Finally, the whole phase transitions in the liquid crystal domain of this ternary system offer a better understanding of the similarities in the local structure of the liquid crystal structures.