The obstructive sleep apnea syndrome (OSAS) is associated to a increased risk of cardiovascular diseases, including stroke. However, it is not known the cause of this last association. In this work the authors carry out a brief review of the theories that explain the relationship between OSAS and stroke and comment the potential alterations in cerebral hemodynamics of sleep apnea syndrome patients. The results of a recent case control study show that there are relevant differences in cerebral blood flow between OSAS patients and healthy subjects even in wakefulness. This fact could help to explain why OSAS causes a higher risk for suffering ischaemic strokes.