To perceive the multiple pitches evoked by simultaneous periodic sounds, the auditory system must estimate their periods. This paper proposes a process in which the periodic sounds are canceled in turn (multistep cancellation model) or simultaneously (joint cancellation model). As an example of multistep cancellation, the pitch perception model of Meddis and Hewitt (1991a,b) can be associated with the concurrent vowel identification model of Meddis and Hewitt (1992). A first period estimate is used to suppress correlates of the dominant sound, and a second period is then estimated from the remainder. The process may be repeated to recursively refine the initial estimates, or else to estimate further pitches. This particular model is spectrotemporal (filter channel selection based on temporal cues) but multistep cancellation can also be performed in the spectral or time domain. In the joint cancellation model, estimation and cancellation are performed together in the time domain: the parameter space of several cascaded cancellation filters is searched exhaustively for a minimum output. The parameters that yield this minimum are the period estimates. Joint cancellation is {\em guaranteed}\ to find all periods, except in certain situations for which the stimulus is inherently ambiguous.