An active medical device that is able to detect and treat ventiliatory activity disorders during sleep. This device measures the patient's respiratory activity, delivers a signal of the ventiliatory activity of the patient, analyzes the ventiliatory activity signal, and detects the occurrence of hypopneas. The analysis includes calculating at regular intervals a sliding average of the signal of ventiliatory activity, comparing the values of the successive sliding averages thus calculated, and detecting an occurrence of an hypopnea when, for two successive sliding averages, the difference between the averages crosses a predetermined threshold of comparison. When the device is one that also delivers cardiac stimulation pulses, it is advantageously envisaged to modify an operating parameter, in particular the stimulation rate based on the detected hypopnea, to treat the hypopnea.