Objective : The aim of our study is to evaluate the consequences of obstructive sleep apnea syndrome on the functional outcome and the survival after an ischemic stroke and to measure the impact of the treatment with continuous positive airway pressure on the outcome of patients with severe obstructive sleep apnea syndrome.Patients and methods : We will prospectively explore by polysomnography, 300 consecutive patients hospitalized for an ischemic stroke in the stroke units of university hospitals at the sub acute phase after stroke (J15±4). 1) We will compare the functional outcome, the neurological impairment, the peripheral endothelial function, the continuous blood pressure measure on 24 hours recording, the quality of life and the survival at 3, 6 and 12 months in four groups of patients depending on their apnea/hypopnea index 2) In patients with severe obstructive sleep apnea syndrome, we will explore the impact on the functional outcome, the neurological impairment, and the survival at 3, 6 et 12 months of a treatment with continuous positive airway pressure (CPAP) randomly compared to a treatment with sham CPAP (non efficacious pressure) during 3 months. Conclusion : This study should allow us to evaluate the consequences of obstructive sleep apnea syndrome on the outcome and the survival after ischemic stroke and the impact and the tolerance of the treatment with continuous positive airway pressure in patients with severe obstructive sleep apnea syndrome.