The measurement of time is fundamental to the perception of complex, temporally structured acoustic signals such as speech and music, yet the mechanisms of temporal sensitivity in the auditory system remain largely unknown. Recently, temporal feature detectors have been discovered in several vertebrate auditory systems. For example, midbrain neurons in the fish Pollimyrus are activated by specific rhythms contained in the simple sounds they use for communication. This poses the significant challenge of uncovering the neuro-computational mechanisms that underlie temporal feature detection. Here we describe a model network that responds selectively to temporal features of communication sounds, yielding temporal selectivity in output neurons that matches the selectivity functions found in the auditory system of Pollimyrus. The output of the network depends upon the timing of excitatory and inhibitory input and post-inhibitory rebound excitation. Interval tuning is achieved in a behaviorally relevant range (10 to 40 ms) using a biologically constrained model, providing a simple mechanism that is suitable for the neural extraction of the relatively long duration temporal cues (i.e. tens to hundreds of ms) that are important in animal communication and human speech.