This paper describes the numerical solution of unsteady flow in the exhaust pipe system of supercharged diesel engines. The solution takes into account the change of specific heats that can occur in the flowing gas. A combination of two well-known methods is used. The flow in the pipe system is solved by the two-step differential Lax-Wendroff method while the boundary conditions are solved by the method of characteristics. The results show that the variation of the specific heats mainly influences the temperature development just upstream of the turbine of the turbocharger. Thus, with this method it is possible to determine more precisely the total mass flow, turbine output parameters and the matching point of the turbocharger.