A mathematical model of joint operation of a piston engine with pulse turbine drive, compressor as well as air supply of a diesel locomotive is presented in the article. This model in an integral part of the complex engine-generator power unit of a diesel locomotive in steady states and transient conditions, developed by the authors. The periodic process in the exhaust manifold is represented as two specific characteristic ranges which encompass the process of forced exhaust and the scavenging process. The scavenging calculation is carried out jointly with the processes taking place in the inlet manifold of the engine, including inlet devices of the locomotive. The process of forced exhaust is calculated separately from the inlet processes and doesn`t require usage of empirical coefficients of impulsiveness. Both processes are represented as systems of nonlinear algebraic equations describe in the quasi-steady flow of working fluid in the elements of the inlet and exhaust tracts. The gas-dynamic calculation of the turbine in the transition process is conducted while taking into account changes in flow angles on the rotor blades. As a result of numerical calculation of the a8S22W diesel operational indices in transient modes, a satisfactory compliance of the calculated and the experimental results was obtained.