The phase behavior of two anionic surfactant systems, one containing a commercial alpha olefin sulfonate (AOS) and the other containing pure sodium dodecyl sulfate (SDS), was determined in the region where a transition from microemulsion to liquid-crystalline phases occurred with decreasing alcohol content and temperature. A general and rather complex pattern of phase behavior was seen that included a four-phase coexistence region of brine, microemulsion, lamellar liquid crystal, and oil, and two phases three-phase regions containing both microemulsion and liquid crystal. In much of the four-phase region, complete separation of the phases did not occur even after equilibrium for 1 year or more at constant temperature. Instead, oil and brine were observed to coexist with stable birefringent dispersions that (for some compositions at least) apparently contained three phases: microemulsion, liquid crystal, and oil. Solubilitization of brine was uniformly low in the phases making up the dispersions. No plugging or other adverse behavior was seen when such dispersions flowed at a velocity of 10-5 m/s [3 ft/D] through a model porous medium having pore sizes comparable with those in reservoirs. In preliminary experiments, selected dispersions appeared to be capable of displacing oil from the same model porous medium.