ABSTRACT Many flow problems encountered in petroleum reservoir engineering are characterized by nonlinearities and are difficult to solve analytically. The concept of a relative mass flow rate function is used to arrive at an integral equation formulation for some of these nonlinear flow problems. This formulation has some distinct advantages over existing methods of handling such nonlinear flow problems because of its generality and simplicity. The problems considered include two-phase fluid displacement including the effect of capillary pressure and isothermal transient flow of gas. These problems can be described by nonlinear parabolic partial differential equations that have self-similar solutions. Exact semi-analytical solutions are obtained which can be easily evaluated using a rapidly-converging iteration process. A new understanding of the mechanism of the displacement of a non-wetting phase by a wetting phase has been developed that is dependent on a critical value of the dimensionless injection rate constant.