A method is described for estimating the fundamental frequencies of several concurrent sounds in polyphonic music and multiple-speaker speech signals. The method consists of a computational model of the human auditory periphery, followed by a periodicity analysis mechanism where fundamental frequencies are iteratively detected and canceled from the mixture signal. The auditory model needs to be computed only once, and a computationally efficient strategy is proposed for implementing it. Simulation experiments were made using mixtures of musical sounds and mixed speech utterances. The proposed method outperformed two reference methods in the evaluations and showed a high level of robustness in processing signals where important parts of the audible spectrum were deleted to simulate bandlimited interference. Different system configurations were studied to identify the conditions where pitch analysis using an auditory model is advantageous over conventional time or frequency domain approaches.