A systematic algorithm for determining the output frequencies generated by a nonlinear system subject to a general multi-tone input, including a bias input, is presented. The algorithm is very efficient, and circumvents many of the difficulties of 'duplicate frequencies' that are often generated using previous methods. The inclusion of the dc bias component in the analysis is also important because of the significant effect that non-zero mean inputs can have on nonlinear system response. The algorithm is straightforward to implement on a computer, and the results are illustrated by means of an example.