Abstract: An automobile stabilizing assembly consisting of a hydraulic fluid filled right cylinder, the interior space of the right cylinder having first, second, and third walls, such walls dividing the right cylinder into first and second chambers, the first and second walls having a piston shaft apertures therethrough, the right cylinder having first and second hydraulic fluid exchange ports extending into its first chamber; a right piston assembly having first and second pistons slidably mounted within the chambers of the right cylinder, and a right piston shaft extending through the piston shaft apertures, the right piston shaft interconnecting the first and second pistons, the second piston having motion damping apertures extending therethrough, the first piston being positioned for sliding motion between the first and second hydraulic fluid exchange ports; a left cylinder similarly configured with the right cylinder; a left piston assembly within the left cylinder, the left piston assembly being similarly config