A method is presented for the determination of ordinary differential equations to describe the performance of existing lumped-parameter, time-invariant, nonlinear physical systems. It is assumed initially that the nonlinear elements can be described by products of continuous functions of system variables and these system variables themselves, which consist of the input and output of the system and their time derivatives. It is also assumed that the system input may be specified and that the output can be measured. The method yields graphical representations of unknown nonlinear functions in an assumed system differential equation. Examples illustrating the accuracy of the procedure are presented, and results obtained in the identification of two physical systems are given.