Classical fractional flow theory is generalized, starting with the Buckley-Leverett theory for waterflooding. The mathematics are based on the method of characteristics. The physics and how the problems are treated are analogous to the multicomponent adsorption problem of chromatography; thus, the methods of Helfferich apply. Enhanced oil-recovery (EOR) cases considered are polymer flooding, carbonated waterflooding, hot waterflooding, hydrocarbon miscible flooding, low-tension flooding, and micellar/polymer flooding. The alcohol flooding, enriched gas, and carbon dioxide cases are analogous in many respects to the micellar/polymer case. Finally, three-phase flow problems are treated. Three-phase flow occurs in a variety of EOR processes.