A generalized non-linear network theory is outlined which enables the behaviour of a given lumpod dynamical system to be described in terms of a set of first-order non-linear differential equations formed in a systematic way, After outlining this theory for systems without interaction between components it is shown how interaction between components may be included in the analysis procedure. As a simple example of the use of the theory, an equation set is derived for the rotor angles of a set ofnsynchronous machines in parallel. An important use of sets of equations of the type derived is in the qualitative analysis of system stability using Lyapunov's direct method. A simple illustrative example of the procedure is given for the case of one synchronous machine connected to an equivalent system represented by another synchronous machine. The chief use of methods of this sort is considered to lie in accurate simulation studies; it is possible however that the scalar functions of system performance used may be of value in coordinated governor and excitation control systems using on-line computers.