The 2-D Laguerre model of the grain growth process as the evolution of a simple convex polygonal complex is generalized to the case of a heterogeneus system. Due to the existence of several types of grains in the system, the specific grain boundary energy depends on the types of neighboring grains. As in other similar studies, the driving force is supposed to be the result of the system's free energy decreasing. We present simulation results of the case where two types of grains are present and exhibit the parametric behavior predicted by Cahn (1). We verify in particular that there are configurations of such a system, where concentration of both types of grains show a damped oscillatory behavior.