Some patients with obstructive sleep apnea (OSA) develop persistent central sleep apnea activity when started on continuous positive airway pressure (CPAP). This recently recognized syndrome, complex sleep apnea syndrome (CompSAS), is thought to be due to dysfunction of the respiratory center in a setting of an obstructive sleep apnea. We present the current knowledge on epidemiology, pathophysiology, and treatment options in CompSAS. We review the current literature on CompSAS, and present our own data on this interesting condition.