A new approach for the segregation of monaural sound mixtures is presented based on the principle of temporal coherence and using auditory cortical representations. Temporal coherence is the notion that perceived sources emit coherently modulated features that evoke highly-coincident neural response patterns. By clustering the feature channels with coincident responses and reconstructing their input, one may segregate the underlying source from the simultaneously interfering signals that are uncorrelated with it. The proposed algorithm requires no prior information or training on the sources. It can, however, gracefully incorporate cognitive functions and influences such as memories of a target source or attention to a specific set of its attributes so as to segregate it from its background. Aside from its unusual structure and computational innovations, the proposed model provides testable hypotheses of the physiological mechanisms of this ubiquitous and remarkable perceptual ability, and of its psychophysical manifestations in navigating complex sensory environments.