We present a novel approach using both sustained vowels and connected speech, to detect obstructive sleep apnea (OSA) cases within a homogeneous group of speakers. The proposed scheme is based on state-of-the-art GMM-based classifiers, and acknowledges specifically the way in which acoustic models are trained on standard databases, as well as the complexity of the resulting models and their adaptation to specific data. Our experimental database contains a suitable number of utterances and sustained speech from healthy (i.e control) and OSA Spanish speakers. Finally, a 25.1% relative reduction in classification error is achieved when fusing continuous and sustained speech classifiers.