In general, spherical or rod micelles in aqueous micellar solution (W-m) or hexagonal liquid crystalline (H-1) phases of hydrophilic ionic surfactant change to a bilayer structure of lamellar liquid crystal (L-alpha) upon addition of amphiphilic oil such as higher alcohol, because such an amphiphilic molecule penetrates in the surfactant palisade layer and the surfactant layer curvature becomes less positive. When an N-acylamino acid derivative oil (N-acylamino acid ester, AAE) such as isopropyl N-dodecanoylsarcosinate (sarcosine N-lauroyl isopropyl, SLIP) is added to sodium dodecyl sulfate (SDS) aqueous solution, a similar phase transition takes place. It was found, however, that the surfactant layer curvature changes in an opposite way from Hi to a discontinuous cubic phase (I-1) upon addition of SLIP in the N-acylamino acid based surfactant sodium N-dodecanoylsarcosinate (Sar) instead of SDS. The I-1 phase consists of discrete micelles, and its structure is indexed to the Fm3m or F23 space group and confirmed by SAXS measurement. Since the headgroup of the N-acylamino acid surfactant is bulkier than that of SDS or EO nonionic surfactant, repulsion between the headgroups may be larger, Therefore, the different phase transition takes place upon addition of SLIP in order to reduce the headgroup repulsion. When SLIP is replaced with a more hydrophilic AAE such as ethyl N-dodecanoylsarcosinate (sarcosine N-lauroyl ethyl, SLET) or N,N'-bis(2-hydroxyethyl)dodecanamide (LEA), the normal phase transition from H-1 to L-alpha takes place because their penetration tendencies are higher and overcome the increase in the headgroup repulsion.