Understanding the dynamics of pathological tremors (e.g., Parkinson’s Disease, Essential Tremor) is crucial to developing effective treatments for these neurological disorders. This paper studies the data-driven modeling of periodic and quasiperiodic tremors. A general neuromusculoskeletal model is proposed to serve as the theoretical basis of this study. The Parkinsonian tremor data is first observed in terms of periodicity, frequency composition, and chaotic characteristics, which confirm tremor is a nonlinear dynamics problem. Two data-driven models are then proposed to predict the nonlinear dynamics of tremor: (1) a model-free approach via long short-term memory recurrent neural network, and (2) a model-based approach via extended dynamical mode decomposition. These models are compared to existing models and the results show that the proposed models outperform existing models for long term prediction of tremor.