CO2 floods at temperatures typically below 120°F can involve complex phase behavior, where a third CO2-rich liquid (L 2) phase coexists with the oleic (L1) and gaseous (V) phases. Results of slim-tube measurements in the literature show that an oil displacement by CO2 can achieve high displacement efficiency of more than 90% when three hydrocarbon-phases coexist during the displacement. However, the mechanism for the high displacement efficiency is uncertain because the complex interaction of phase behavior with flow during the displacement is not fully understood. In this paper, we present the first detailed study of three-phase behavior predictions and displacement efficiency for low-temperature CO2 floods. Four-component EOS models are initially used to investigate systematically the effects of pressure, temperature, and oil properties on development of three-phase regions and displacement efficiency. Multicomponent oil displacements by CO2 are then considered. We use a compositional reservoir simulator capable of robust three-phase equilibrium calculations. Results show that high displacement efficiency of low-temperature CO2 floods is a consequence of both condensing and vaporizing behavior. The L2 phase serves as a buffer between the immiscible V and L1 phases within the three-phase region. Components in the L 1 phase first transfer efficiently to the L2 phase near a lower critical endpoint (LCEP). These oil components then transfer to the V phase near an upper critical endpoint (UCEP) at the trailing edge of the three-phase region. The CEPs are defined where two of the three coexisting phases merge in the presence of the other immiscible phase Unlike two-phase displacements, condensation and vaporization of intermediate components occur simultaneously within the three-phase region. The simultaneous condensing/vaporizing behavior involving the CEPs is also confirmed for simulations of several west Texas oil displacements. Quaternary fluid models can predict qualitatively the complex displacements because four is the minimum number of components to develop CEP behavior in composition space at a fixed temperature and pressure.