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Introduction: Obstructive sleep apnea (OSA) can cause serious health problems such as hypertension or cardiovascular disease. The manual detection of apnea is a time-consuming task, and automatic diagnosis is much more desirable. The contribution of this work is to detect OSA using a multi-error-reduction (MER) classification system with multi-domain features from bio-signals. Methods: Time-domain, frequency-domain, and non-linear analysis features are extracted from oxygen saturation (SaO2), ECG, airflow, thoracic, and abdominal signals. To analyse the significance of each feature, we design a two-stage feature selection. Stage 1 is the statistical analysis stage, and Stage 2 is the final feature subset selection stage using machine learning methods. In Stage 1, two statistical analyses (the one-way analysis of variance (ANOVA) and the rank-sum test) provide a list of the significance level of each kind of feature. Then, in Stage 2, the support vector machine (SVM) algorithm is used to select a final feature subset based on the significance list. Next, an MER classification system is constructed, which applies a stacking with a structure that consists of base learners and an artificial neural network (ANN) meta-learner. Results: The Sleep Heart Health Study (SHHS) database is used to provide bio-signals. A total of 66 features are extracted. In the experiment that involves a duration parameter, 19 features are selected as the final feature subset because they provide a better and more stable performance. The SVM model shows good performance (accuracy = 81.68%, sensitivity = 97.05%, and specificity = 66.54%). It is also found that classifiers have poor performance when they predict normal events in less than 60 s. In the next experiment stage, the time-window segmentation method with a length of 60 s is used. After the above two-stage feature selection procedure, 48 features are selected as the final feature subset that give good performance (accuracy = 90.80%, sensitivity = 93.95%, and specificity = 83.82%). To conduct the classification, Gradient Boosting, CatBoost, Light GBM, and XGBoost are used as base learners, and the ANN is used as the meta-learner. The performance of this MER classification system has the accuracy of 94.66%, the sensitivity of 96.37%, and the specificity of 90.83%.