Inertial suspension magnetic stabilizer that complements the suspension of vehicles and mobiles of different nature, opposing and compensating inertially to sudden impulses; mountable to wheel cups or to the wheel axis support, preferably constructed in a body preferably forming a hollow cylinder containing gaseous or liquid fluids, composed of a hermetic tubular body provided at its ends with fixed magnets and in its central area of a magnetically neutral sliding piston, supported by its magnet ends with equal polarity, facing, to that of the magnets fixed at the ends of the tubular body; sliding piston that in turn divides the tubular body into two hermetic chambers linked together, by a tube provided with a fluid regulating valve.