The article presents the differential equations of a synchronous generator in phase coordinates and in the coordinate system (d, q). In addition, differential equations of synchronous machines with longitudinal-transverse excitation and a block diagram based on these equations are given. The system of differential equations is solved by the operator method. On the basis of a system of differential equations using the Simulink Matlab program, a structural diagram was created and a graph of the self-swinging processes taking place in synchronous machines with conventional and longitudinal-transverse excitation was obtained. On the basis of the obtained graph, the processes of self-swinging of synchronous generators with traditional and longitudinal and transverse excitation are compared.