Continuous positive airway pressure (CPAP) therapy of obstructive sleep apnea syndrome (OSAS) is widely accepted. Recently it is reported that central type apnea increases in some patients with OSAS with the application of CPAP, and this type of sleep-disordered breathing is called complex sleep apnea syndrome (comp. SAS). However, until now its concept, mechanism and therapy have not been fully established. We treated 2 cases of comp. SAS with CPAP therapy. When we performed a polysomnography (PSG) examination in case 1 one year later, the symptoms had diminished and the central apnea had decreased, indicating the effectiveness CPAP therapy in case 1. In case 2, the symptoms had not diminished one year later. We therefore performed Adaptive Servo-Ventilation (ASV) therapy, resulting in improvement of symptoms and decrease of the central apnea. CPAP is not always effective in comp. SAS, and ASV can be suitable in such cases.