Obstructive sleep apnea (OSA) is a sleep disorder that causes partial or complete cessation of breathing during an individual's sleep. Various methods have been proposed to automatically detect OSA events, but little work has focused on predicting such events in advance, which is useful for the development of devices that regulate breathing during a patient's sleep. We propose four methods for sleep apnea prediction based on convolutional and long short-term memory neural networks (1D-CNN, ConvLSTM, 1D-CNN-LSTM and 2D-CNN-LSTM), which use raw data from three respiratory signals (nasal flow, abdominal and thoracic) sampled at 32 Hz, without any human-engineered features. We predict OSA (apnea or hypopnea) and normal breathing events 30 seconds ahead using the prior 90 seconds' data. Our results on a dataset containing over 46,000 examples from 1,507 subjects show that all four models achieved promising accuracy ( 81%). The 1D-CNN-LSTM and 2D-CNN-LSTM were the best two performing models with accuracy, sensitivity and specificity over 83%, 81% and 85% respectively. These results show that OSA events can be accurately predicted in advance based on respiratory signals, opening up opportunities for the development of devices to preemptively regulate the airflow to sleepers to avoid these events. Furthermore, we demonstrate good prediction performance even when respiratory signals are downsampled by a factor of 32, to 1 Hz, for which our proposed 1D-CNN-LSTM achieved 82.94% accuracy, 81.25% sensitivity and 84.63% specificity. This robustness to low sampling frequencies allows our algorithms to be implemented in devices with low storage capacity, making them suitable for at-home environments.