Individuals tend to anticipate the beat when moving to sound, and this anticipatory synchronization can be captured by nonlinear dynamical systems. In this study, unidirectional delay-coupling oscillator models with intrinsic frequency (ω), time delay (τ) and coupling strength (κ) parameters were used to capture the behaviour of musically untrained and trained participants in a synchronization task. Participants first tapped a melody at a steady, uncued rate (their spontaneous production rate, or SPR). Then, they synchronized their tapping with an auditory metronome cued at different rates (their own SPR or their partner’s SPR) and in a Solo or Joint (turn-taking) condition. The delay-coupling models were compared with linear models (without time delay or coupling). All models were fit to half of the asynchronies (signed timing differences between the metronome onsets and taps) from each trial (Train data), then applied to the other half (Test data) as well as to matched data from other pairs of participants (Surrogate data). Delay-coupling models performed better (higher correlation between predicted and observed asynchronies) than linear models. Delay-coupling models also had better outcomes for Test data than for Surrogate data, suggesting that these models generalize well. In comparison, linear models did not differ for Test and Surrogate outcomes, suggesting that the linear models were not able to generalize. These findings indicate that delay-coupling models can capture individual differences in auditory-motor synchronization. Cross-validation combined with surrogate comparisons offers promise for assessing nonlinear models of synchronization.