The primary endpoint of the trial is to compare the treatment efficacy of CPAP and MAD in Veterans with PTSD and OSA. Secondary endpoints aim at: 1) comparing change in the Epworth Sleepiness Scale, SF-36, and the Pittsburgh Sleep Quality Index at end of treatment following use of CPAP versus MAD, 2) comparing adherence and short-term side effects between using CPAP and MAD in PTSD patients with OSA, and 3) determining anthropomorphic, polysomnographic, and cephalometric predictors of successful MDA response. Assessments at the end of both limbs comprise evaluation of quality of sleep, daytime sleepiness, quality of life, and side effects of treatment. Compliance with each therapy will be measured at the end of each treatment period.