 In the second stage patients with OHS will be divided into two subgroups: group 1: patients with polysomnography PSG suggestive of hypoventilation, in whom NIV treatment will be initiated; group 2: patients with PSG suggestive of OSAHS apnea-hypopnea index 15, who will be administered CPAP. Patients will be examined one month and three months after the start of treatment. The same measurements will be carried out as at the beginning of the study, with the exception of the polysomnographic study. Nonetheless, pulse oximetry and arterial gases will be performed on waking. 