Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS) is a sleep related breathing disorder that has important consequences in the health and development of infants and young children. To enhance the early detection of OSAHS, we propose a methodology based on automated analysis of nocturnal blood oxygen saturation (SpO(2)) from respiratory polygraphy (RP) at home. A database composed of 50 SpO(2) recordings was analyzed. Three signal processing stages were carried out: (i) feature extraction, where statistical features and nonlinear measures were computed and combined with conventional oximetric indexes, (ii) feature selection using genetic algorithms (GAs), and (iii) feature classification through logistic regression (LR). Leave-one-out cross-validation (loo-cv) was applied to assess diagnostic performance. The proposed method reached 80.8% sensitivity, 79.2% specificity, 80.0% accuracy and 0.93 area under the ROC curve (AROC), which improved the performance of single conventional indexes. Our results suggest that automated analysis of SpO(2) recordings from at-home RP provides essential and complementary information to assist in OSAHS diagnosis in children.