The brain uses temporal structure in the environment, like rhythm in music and speech, to predict the timing of events, thereby optimizing their processing and perception. Temporal expectations can be grounded in different aspects of the input structure, such as a regular beat or a predictable pattern. One influential account posits that a generic mechanism underlies beat-based and pattern-based expectations, namely, entrainment of low-frequency neural oscillations to rhythmic input, whereas other accounts assume different underlying neural mechanisms. Here, we addressed this outstanding issue by examining EEG activity and behavioral responses during silent periods following rhythmic auditory sequences. We measured responses outlasting the rhythms both to avoid confounding the EEG analyses with evoked responses, and to directly test whether beat-based and pattern-based expectations persist beyond stimulation, as predicted by entrainment theories. To properly disentangle beat-based and pattern-based expectations, which often occur simultaneously, we used non-isochronous rhythms with a beat, a predictable pattern, or random timing. In Experiment 1 (n = 32), beat-based expectations affected behavioral ratings of probe events for two beat-cycles after the end of the rhythm. The effects of pattern-based expectations reflected expectations for one interval. In Experiment 2 (n = 27), using EEG, we found enhanced spectral power at the beat frequency for beat-based sequences both during listening and silence. For pattern-based sequences, enhanced power at a pattern-specific frequency was present during listening, but not silence. Moreover, we found a difference in the evoked signal following pattern-based and beat-based sequences. Finally, we show how multivariate pattern decoding and multiscale entropy—measures sensitive to non-oscillatory components of the signal—can be used to probe temporal expectations. Together, our results suggest that the input structure used to form temporal expectations may affect the associated neural mechanisms. We suggest climbing activity and low-frequency oscillations may be differentially associated with pattern-based and beat-based expectations.