We present a method for determining a model of the formSMfrom measurements on the steady-state response of a non-linear system to co-sinusoidal inputs at a number of amplitudes and frequencies. In earlier papers the parameter identifiability of theSMstructure for this type of input/output experiment was established using an interpolation approach. Here we use a harmonic analysis technique to choose linear subsystems in the model and then minimization of an integral square-error criterion to select certain free coefficients within these subsystems. The results are illustrated by application to a forced Duffing equation and a forced Van der Pol equation.