The output response of nonlinear systems is strongly dependent on the extent to which different input frequency combinations/intermodulations overlap one another and contribute to a common output frequency component. This makes it hard to determine the actual number of output frequencies, or to determine which of the many possible combinations contribute to a specified output frequency of interest. Systematic algorithms are presented for resolving these issues in a manner, which is both efficient and straightforward to implement on a computer. Three broad classes of input are considered: multi-tone, but nominally incommensurate sinusoids; multi-tone, harmonically related sinusoids and multi-tone excitations that are equi-spaced in frequency. The considered inputs also admit the possibility of a dc bias component since this can significantly affect the system response. The algorithms are therefore applicable to a broad range of practical inputs, and their use and benefits are illustrated with several examples.