THE RELATIVE DIFFICULTY of on-beat and off-beat finger tapping with simple auditory rhythms was assessed in four experiments with musically trained participants. The rhythms consisted of cyclically repeated TT0 or TTT0 patterns, where T denotes the presence and 0 denotes the absence of a tone. The tasks were to tap in synchrony with one of the T ("on-beat") positions or with the 0 ("off-beat") position. Experiments 1-3 used an adaptive procedure that determined the fastest tempo at which each task could be accomplished. Experiment 1 demonstrated that it is easier to tap on tones that carry a rhythmic grouping accent (T2 in TT0, T1 and T3 in TTT0) than on other tones or in the 0 position. Off-beat tapping was more difficult in TT0 than in TTT0 sequences. Experiment 2 showed that a dynamic ( pitch) accent on one of the tones facilitates synchronization with that tone and impedes synchronization with adjacent tones. Off-beat tapping was less affected by accent location. Experiment 3 required participants to "hear" different T positions as metrically accented (i.e., to construe them as the downbeat) while carrying out the various tapping tasks. Most participants found it difficult to maintain a cognitive downbeat at fast tempi when it did not coincide with their taps. However, when such a downbeat could be maintained, it did not seem to increase the difficulty of tapping (with one exception). This suggests a unidirectional dependence of metrical structure on action. In Experiment 4, the same tasks were presented at more moderate tempi, and the dependent measure was the variability of asynchronies. Metrical downbeat location still did not have any significant effect. Thus, synchronization difficulty seems to be affected only by a rhythm's physical structure, not by the cognitive interpretation that is given to that structure.