An active medical device, in particular an implantable device such as a cardiac pacemaker, defibrillator, cardioverter, or multisite device, including a function for determining sleep disorders. This device can collect the heartbeat rhythm in at least one heart cavity, and analyze the collected rhythm so as to evaluate a value of heartbeat rate accordingly. The device can also discriminate within a collected heart rhythm the spontaneous events of sinusal origin, and to evaluate the heart rate according only to these spontaneous sinusal events, and to analyze the time variations of the aforementioned heart rate to determine the presence of a sleep respiratory disorder accordingly. This analysis can be realized through a search for episodes of bradycardia followed by episodes of tachycardia, or by determination of an index of sinusal variability that is a function of the detected variations, and comparison of this index with a predetermined threshold.