This paper is concerned with a model of the longitudinal dispersion of a set of tagged particles in a flow through nonhomogeneous stratified porous media. The model is a particular homogeneous Markov jump process, the successive states visited forming a non-homogeneous Poisson process. The passage time of alevel x of this Markov process is an additive stochastic process.This property is used to evaluate the general form of the longitudinal concentration function of the tagged particles in the flow.