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Patients suspected of suffering sleep apnea and hypopnea syndrome (SAHS) have to undergo sleep studies such as expensive polysomnographies to be diagnosed. Healthcare professionals are constantly looking for ways to improve the ease of diagnosis and comfort for this kind of patients as well as reducing both the number of sleep studies they need to undergo and the waiting times. Relating to this scenario, some research proposals and commercial products are appearing, but all of them record the physiological data of patients to portable devices and, in the morning, these data are loaded into hospital computers where physicians analyze them by making use of specialized software. In this paper, we present an alternative proposal that promotes not only a transmission of physiological data but also a real-time analysis of these data locally at a mobile device. For that, we have built a classifier that provides an accuracy of 93% and a receiver operating characteristic-area under the curve (ROC-AUC) of 98.5% on SpO2 signals available in the annotated Apnea-ECG Database. This local analysis allows the detection of anomalous situations as soon as they are generated. The classifier has been implemented taking into consideration the restricted resources of mobile devices.