Flow of two and three immiscible fluids in porous media is considered in which the various fluids are separated into different saturation zones by gravity. An equation of flow for any one fluid is derived with the condition that the other fluids must be stationary. This equation is then applied to solve the question of the maximum rate of flow of one fluid into a well from a radially symmetrical porous medium without producing the other fluid or fluids present in the formation. Different well geometries and fluid systems are considered. These problems are sometimes called ``coning'' problems.