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Obstructive Sleep Apnea (OSA) is a respiratory disorder with serious consequences that is characterized by repetitive cessation of breathing for more than 10s often associated with a drop of more than 4% in the blood's Oxygen saturation level. The gold standard for OSA diagnosis is full-night Polysomnography (PSG), which is a time-consuming, inconvenient, and costly assessment. On the other hand, our team has showed that the analysis of tracheal respiratory sounds recorded during wakefulness holds promises to be used as a simple and effective tool for screening moderate and severe OSA. In this paper, we examine the nonlinear characteristics of tracheal breath sounds and the possibility to extract features from Higher Order Spectra (HOS) for OSA screening. The data used in this study were recorded during wakefulness in two body positions, supine and upright, and during mouth and nose breathing. We estimated the bispectrum of the sounds in each respiratory cycle, calculated the median bifrequencies and the energy of the bispectrum, and investigated any statistically significant differences between the extracted features in two groups of non-OSA and severe OSA data. The differences in the features between body positions and nose/mouth breathing were also looked at. One-way ANOVA revealed significant differences in the features between non-OSA individuals and those with severe OSA. The results encourage the use of these features in future studies for OSA screening.