Title: Oscillation Neural Ordinary Differential Equations. Abstract: Neural ordinary differential equations (NODEs) have received a lot of attention in recent years due to their memory efficiency. Different from traditional deep learning, it defines a continuous deep learning architecture based on the theory of ordinary differential equations (ODEs), which also improves the interpretability of deep learning. However, it has several obvious limitations, such as a NODE is not a universal approximator, it requires a large number of function evaluations (NFEs), and it has a slow convergence rate. We address these drawbacks by modeling and adding an oscillator to the framework of the NODEs. The oscillator enables the trajectories of our model to cross each other. We prove that our model is a universal approximator, even in the original input space. Due to the presence of oscillators, the flows learned by the model will be simpler, thus our model needs fewer NFEs and has a faster convergence speed. We apply our model to various tasks including classification and time series extrapolation, then compare several metrics including accuracy, NFEs, and convergence speed. The experiments show that our model can achieve better results compared to the existing baselines.