The determination of the number of signals in a wide class of problems, including array processing, harmonic retrieval and pole retrieval, is addressed. A new approach, based on the application of the information theoretic criteria for model identification introduced by Akaike, Schwartz and Rissanen, is presented. It is shown that the criterion introduced by Schwartz and Rissanen yields a consistent estimate of the number of signals, while the criterion introduced by Akaike yields an inconsistent estimate that tends, in the large-sample limit, to overestimate the number of signals.