Abstract: The invention relates to an active implantable medical device. The device measures for respiratory activity and for detection of a ventilation rate fall event below a predetermined threshold. The device analyzes in real time the various parameters of the ventilation rate fall event and determines whether they satisfy predefined criteria, so as to allocate or not a priori hypopnea suspicion indicator to the event. An anti-hypopnea therapy is selectively triggered on detection of respiratory collapse, but only in the case of current events indicating a priori hypopnea suspicion. The criteria may include: history of intervals between successive events constituting hypopnea episodes; severity of the current event; conformity of a current event profile with a reference profile; physiological, obstructive or central, origin of the event; patient's current sleep stage; and history of the degree of efficacy of the therapies.