Abstract: In this paper we study front tracking for a model of one dimensional, immiscible flow of several isentropic gases, each governed by a gamma-law. The model consists of the $p$-system with variable gamma representing the different gases. The main result is the convergence of a front tracking algorithm to a weak solution, thereby giving existence as well. This convergence holds for general initial data with a total variation satisfying a specific bound. The result is illustrated by numerical examples.