Abstract: An active implantable medical device, particularly a cardiac pacemaker, which is enslaved to a signal representative of acceleration, having a measuring circuit (10) comprising at least one sensor (12) delivering a signal of acceleration, and circuits (22-24) to deliver, in response to the signal of acceleration, a parameter of enslavement of at least one function of the device, particularly that of a cardiac stimulation frequency. According to the invention, a circuit (24) operates to limit, in the detection of increase in acceleration, a value linked to the module of the signal of acceleration. Preferably, the limitation is operated on a value proportional to the square of the signal of acceleration, more particularly on a quadratic sum of individual acceleration components (X.sub.i, Y.sub.i, Z.sub.i) according to at least two distinct axes delivered by a respective number of sensors.