Sleep disturbances are cardinal features of Veterans with post traumatic stress disorder (PTSD). In particular, obstructive sleep apnea is reported to occur more frequently in patients with PTSD compared to those without PTSD and contribute to worsening cognitive and behavioral functions. Continuous positive airway pressure (CPAP) is considered the treatment of choice for OSA but adherence to CPAP in Veterans with PTSD is poor compared to the general population. The proposed study aims at comparing the efficacy, tolerability, and adherence of oral appliances-an alternative therapy to OSA- to CPAP. The study is instrumental in identifying the optimal OSA therapy for Veterans with PTSD and the OSA phenotype that would predict oral appliance response