Objective: We present a system for automated annotation of non-apnoea arousals using twelve signals from the polysomnogram (PSG) including airflow, six signals of electroencephalogram, the electrooculogram, chin electromyogram, oximetry signal, and chest and abdominal respiratory effort signals. Approach: Fifty-nine time- and frequency-domain features were extracted from the twelve signals using 15 s epochs. Features from an epoch were combined with features from adjacent epochs and then processed with a bank of feed-forward networks that provided a probability estimate of the occurrence of a non-apnoea arousal event in every epoch. Data from the 2018 PhysioNet/Computing in Cardiology Challenge was used to develop and test the system. Ten-fold cross validation on the 994 PSGs of training data was used to compare the performance of different network configurations. Main results: Our highest performing configuration utilised a bank of 30 feed-forward neural networks. Each network processed ±4 epochs of features and each used a single hidden layer of 20 units. The performance of this configuration was evaluated on the independent test set of 989 PSGs and achieved an area under the receiver operator curve of 0.848 and an area under the precision-recall curve of 0.325 for correctly discriminating non-apnoea arousals from non-arousals samples. Significance: The classification performance results of our system demonstrate that automated annotation of non-apnoea arousals can be achieved with a high degree of reliability.