A generalized Flory-Huggins theory is described that permits the investigation of the phase behavior for quasi-binary polymer solutions or blends in which, for blends, both components may be polydisperse. A temperature- and concentration-dependent chi interaction parameter is used. It is demonstrated that the chi parameter may be readily extracted from experimental phase data. This is illustrated by using a robust fitting procedure to obtain the composition and temperature dependence of chi for the cyclochexane/polystyrene system from experimental phase data. The result (eq 22) is in excellent agreement with previous determinations of chi for this system, and the method employed here has several advantages over other approaches. Relative merits of a number of methods are discussed. The composition- and temperature-dependent chi determined here (eq 22) is used to predict cloud-point curves for solutions of polystyrene with various bimodal distributions in cyclohexane. These computed CPCs are found to be in quantitative agreement with experimental data.