Prediction of nonlinear and dynamic systems is a challenging task, however with the aid of machine learning techniques, particularly neural networks, is now possible to accomplish this objective. Most common neural networks used are the multilayer perceptron (MLP) and recurrent neural networks (RNN) using long-short term memory units (LSTM-RNN). In recent years, deep learning neural network models have become more relevant due the improved results they show for various tasks. In this paper the authors compare these neural network models with deep learning neural network models such as long-short term memory deep recurrent neural network (LSTM-DRNN) and gate recurrent unit deep recurrent neural network (GRU-DRNN) when presented with the task of predicting three different chaotic systems such as the Lorenz system, Rabinovich–Fabrikant and the Rossler System. The results obtained show that the deep learning neural network model GRU-DRNN has better results when predicting these three chaotic systems in terms of loss and accuracy than the two other models using less neurons and layers. These results can be very helpful to solve much more complex problems such as the control and synchronization of these chaotic systems.