Summary: We examine a model for the separation kinetics of a dispersion of two immiscible liquids under the action of gravity. The scalar case (one family of equally sized drops), which is treated first, naturally suggests the guidelines for the vector case (\(n\) families of droplet of different sizes). The general model is governed by a no-symmetric system which is investigated for diluted and concentrated dispersions. In both cases under reasonable hypotheses we prove that the system is strictly hyperbolic, which guarantees local existence and uniqueness of solution.