A chemical flood model for a three-component (petroleum, water, injected chemical) two-phase (aqueous, oleic) system is presented. It is ruled by a system of nonlinear partial differential equations: the continuity equation for the transport of each of its components and Darcy＇s equation for the two-phase flow. The transport mechanisms considered are ultralow interfacial tension, capillary pressure, dispersion, adsorption, and partition of the components between the fluid phases (including solubilization and swelling). The mathematical model is numerically solved in the one-dimensional case by finite differences using an explicit and direct iterative procedure for the discretization of the conservation equations. Numerical results are compared with Yortsos and Fokas＇ exact solution for the linear waterflood case including capillary pressure effects and with Larson＇s model for surfactant flooding. The effects of the above-mentioned transport mechanisms on concentration profiles and on oil recovery are also analyzed.