The influence of the addition of the cationic surfactant cetylpyridinium chloride (CPyCl) on the structure of the different phases of the ternary surfactant system C12E4/benzyl alcohol/water in the dilute region has been studied by means of small angle neutron scattering (SANS) and freeze-fracture microscopy (FF-TEM). In the ternary system various different subregions of the L-alpha-phase were identified as a function of the concentration of the cosurfactant, benzyl alcohol. Addition of small amounts of CPyCl suppresses these different L-alpha-phases in favor of the one composed of multilamellar vesicles. Addition of somewhat larger amounts (up to 2 mol% relative to the total surfactant concentration) destabilizes the formation of bilayer structures completely and leads to the formation of micellar solutions. This demonstrates that in this surfactant system the incorporation of very small amounts of cationic surfactant has a pronounced and systematic fluence on its phase behavior and its structures.