Since studies have revealed sleeping quality is highly related to our health conditions, sleep-medicine has attracted more and more attention in recent years. Sleep staging is one of the most important elements of sleep-medicine. Traditionally, it¡¦s done by observing the information form of EEG, EOG and EMG signals. But this is almost not possible to achieve at home. Automatic detection of REM sleep is the main goal of this study. Via comparing the classification performances of different combinations of EEG, EOG and EMG signals, this study also tries to simplify the number of signal channels. By using features extracted from EEG, EOG and EMG signals, the back-propagation neural networks are used to distinguish REM and NREM sleep. By refining the outputs of the neural networks, this study extensively test the efficacy of the proposed approach by using databases from two different sleep centers. This work also investigates the influences of the number of signal channels, REM sleep ratio, AHI, and age on classification results. Data acquired from the sleep centers of China Medical University Hospital (CMUH) and Sheng-Mei Hospital are arranged in ten different groups. For our largest datasets, which consists of 1318 subjects from CMUH, the results show that the proposed method achieves 95.5% epoch-to-epoch agreement with Cohen's Kappa 0.833, sensitivity 85.9% and specificity 97.3%. The generalization accuracy is 94.1% with Cohen's Kappa 0.782, sensitivity 78.5% and specificity 97.3%.