Algebraic expressions are derived which enable the harmonic balance equations to be written down directly in terms of the coefficients of a general nonlinear difference or differential equation model. The new expressions are particularly useful because they are not restricted to a specific waveform, but apply to the whole class of harmonically related, phase independent, sinusoidal signals. The system frequency response, in the form of a multi-input, amplitude dependent describing function, is therefore readily computed, as illustrated by means of an example.