The diagnosis of obstructive sleep apnea is based on daytime symptoms and the frequency of respiratory events during the night. The respiratory events are scored manually from polysomnographic recordings, which is time-consuming and expensive. Therefore, automatic scoring methods could considerably improve the efficiency of sleep apnea diagnostics and release the resources currently needed for manual scoring to other areas of sleep medicine. In this study, we trained a long short-term memory neural network for automatic scoring of respiratory events using input signals from peripheral blood oxygen saturation, thermistor-airflow, nasal pressure -airflow, and thorax respiratory effort. The signals were extracted from 887 in-lab polysomnography recordings. 787 patients with suspected sleep apnea were used to train the neural network and 100 patients were used as an independent test set. The epoch-wise agreement between manual and automatic neural network scoring was high (88.9%, =0.728). In addition, the apnea-hypopnea index (AHI) calculated from the automated scoring was close to the manually determined AHI with a mean absolute error of 3.0 events/hour and an intraclass correlation coefficient of 0.985. The neural network approach for automatic scoring of respiratory events achieved high accuracy and good agreement with manual scoring. The presented neural network could be used for improving the efficiency of sleep apnea diagnostics or for analysis of large research datasets that are unfeasible to score manually. In addition, since the neural network scores individual respiratory events, the automatic scoring can be easily reviewed manually if desired.