The effect of 1-alkanols upon the main phase-transition temperature of phospholipid vesicle membranes between gel and liquid-crystalline phases was not a simple monotonic function of alkanol concentration. For instance, 1-decanol decreased the transition temperature at low concentrations, but increased it at high concentrations, displaying a minimal temperature. This concentration-induced biphasic effect cannot be explained by the van't Hoff model on the effect of impurities upon the freezing point. To explain this nonlinear response, a theory is presented which treats the effect of 1-alkanols (or any additives) on the transition temperature of phospholipid membranes in a three-component mixture. By fitting the experimental data to the theory, the enthalpy of the phase transition delta H* and the interaction energy, epsilon*AB between the additive and phospholipid molecules may be estimated. The theory predicts that when epsilon*AB greater than 2 (where epsilon*AB = epsilon AB/RT0, T0 being the transition temperature of phospholipid), both minimum and maximum transition temperatures should exist. When epsilon*AB = 2, only one inflection point exists. When epsilon*AB less than 2, neither maximum nor minimum exists. The alkanol concentration at which the transition temperature is minimum (Xmin) depends on the epsilon*AB value: the larger the epsilon*AB values, the smaller the Xmin. When epsilon*AB is large enough, Xmin values become so small that the plot delta T vs. X shows positive delta T in almost all alkanol concentrations. The interaction energy between 1-alkanols and phospholipid molecules increased with the increase in the carbon chain-length of 1-alkanols. In the case of the dipalmitoylphosphatidylcholine vesicle membrane, the carbon chain-length of 1-alkanols that caused predominantly positive delta T was about 12.