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This study focuses on the analysis of blood oxygen saturation (SaO2) from nocturnal pulse oximetry (NPO) to help in the diagnosis of the obstructive sleep apnea (OSA) syndrome. A population of 148 patients suspected of suffering from OSA syndrome was studied. A wide set of 16 features was used to characterize changes in the SaO2 profile during the night. Our feature set included common statistics in the time and frequency domains, conventional spectral characteristics from the power spectral density (PSD) function, and nonlinear features. We performed feature selection by means of a step-forward logistic regression (LR) approach with leave-one-out cross-validation. Second- and fourth-order statistical moments in the time domain (M2t and M4t), the relative power in the 0.014-0.033 Hz frequency band (PR), and the Lempel-Ziv complexity (LZC) were automatically selected. 92.0% sensitivity, 85.4% specificity, and 89.7% accuracy were obtained. The optimum feature set significantly improved the diagnostic ability of each feature individually. Furthermore, our results outperformed classic oximetric indexes commonly used by physicians. We conclude that simultaneous analysis in the time and frequency domains by means of statistical moments, spectral and nonlinear features could provide complementary information from NPO to improve OSA diagnosis.