Multicenter open randomized clinical trial involving 800 patients with severe OSAS. After inclusion in the study, the patients will be proposed to initiate CPAP at home (ResMed S9 or PHILIPS PR1) using systematically an APAP mode between wide range of pressure variations (4 to 20 cm H2O) during the first 7day-period of time. After this first period of treatment, an analysis of the report will be released from the APAP in order evaluate the residual AHI, the duration of CPAP use and the amount of leaks in order to confirm CPAP efficiency and observance. Pressure parameters (efficient pressure and variability) will be collected. After randomization according to the further mode of ventilation to use (APAP vs constant CPAP), the patients will be treated at home for 3 months. In the constant CPAP group, efficient pressure will be determined as the P95 (ResMed) or the P90 (PHILIPS) as recommended by the manufacturers, while in the APAP group, the patients will be treated within the same range of pressure variations than during the first 7 day-period. Clinical and polygraphic evaluation will be done after 3 months of treatment, using the combined criteria previously described. In each group, results will be considered according to the efficient pressure value and its variability that were evaluated at the end of the first 7 day-period of treatment