To probe sensitivity to the time structure of ongoing sound sequences, we measured MEG responses, in human listeners, to the offset of long tone-pip sequences containing various forms of temporal regularity. If listeners learn sequence temporal properties and form expectancies about the arrival time of an upcoming tone, sequence offset should be detectable as soon as an expected tone fails to arrive. Therefore, latencies of offset responses are indicative of the extent to which the temporal pattern has been acquired. In Exp1, sequences were isochronous with tone inter-onset-interval (IOI) set to 75, 125 or 225 ms. Exp2 comprised of non-isochronous, temporally regular sequences, comprised of the IOIs above. Exp3 used the same sequences as Exp2 but listeners were required to monitor them for occasional frequency deviants. Analysis of the latency of offset responses revealed that the temporal structure of (even rather simple) regular sequences is not learnt precisely when the sequences are ignored. Pattern coding, supported by a network of temporal, parietal and frontal sources, improved considerably when the signals were made behaviourally pertinent. Thus, contrary to what might be expected in the context of an ‘early warning system’ framework, learning of temporal structure is not automatic, but affected by the signal's behavioural relevance.