Obstructive sleep apnea (OSA) is a prevalent disorder associated with poor neurocognitive performance and organ system dysfunction due to intermittent hypoxia and repeated arousals. The repetitive hemodynamic stresses are implicated in the increased incidence of systemic hypertension and cardiovascular diseases. Insufficient and disrupted sleep has similar negative impact on mood, attention, cognition, and behavior. In Veterans with post traumatic stress disorder (PTSD), the disturbed sleep can worsen further the cognitive-behavioral manifestations of PTSD and contributes to poor mental and physical health outcomes. Recent epidemiologic studies largely support the association of higher rates of OSA in patients with PTSD compared with the general population. Treatment of the underlying obstructive sleep disturbances with continuous positive airway pressure (CPAP) has resulted in restoration of sleep architecture, decrease daytime sleepiness, and reduction in nightmares frequency and intensity. However, adherence to treatment with CPAP is less than optimal in Veterans with PTSD. Mandibular advancing devices (MADs) are considered non surgical alternatives to CPAP and are preferred in a head to head comparison to CPAP in OSA subjects without PTSD. However, there has been no study to the investigators' knowledge that has assessed MAD in terms of clinical efficacy, compliance, and quality of sleep compared to CPAP in OSA patients with PTSD. Therefore, the investigators hypothesize that MAD is not inferior to CPAP in treating OSA effectively in Veterans with PTSD and OSA. To that end, the investigators propose to conduct a feasibility study using a randomized crossover trial of 12 weeks of CPAP and MAD in 42 consecutive outpatients with PTSD newly diagnosed with OSA separated by 2 weeks washout period.