Normal auditory perception relies on accurate judgments about the temporal relationships between sounds. Previously, we used a perceptual-learning paradigm to investigate the neural substrates of two such relative-timing judgments made at sound onset: detecting stimulus asynchrony and discriminating stimulus order. Here, we conducted parallel experiments at sound offset. Human adults practiced [similar to]1 h/d for 6-8 d on either asynchrony detection or order discrimination at sound offset with tones at 0.25 and 4.0 kHz. As at sound onset, learning on order-offset discrimination did not generalize to the other task (asynchrony), an untrained temporal position (onset), or untrained frequency pairs, indicating that this training affected a quite specialized neural circuit. In contrast, learning on asynchrony-offset detection generalized to the other task (order) and temporal position (onset), though not to untrained frequency pairs, implying that the training on this condition influenced a less specialized, or more interdependent, circuit. Finally, the learning patterns induced by single-session exposure to asynchrony and order tasks differed depending on whether these tasks were performed primarily at sound onset or offset, suggesting that this exposure modified circuitry specialized to separately process relative-timing tasks at these two temporal positions. Overall, it appears that the neural processes underlying relative-timing judgments are malleable, and that the nature of the affected circuitry depends on the duration of exposure (multihour or single-session) and the parameters of the judgment(s) made during that exposure.