The present invention relates to the front suspension containing elastic (14) and damping (11) elements, for vehicles with front steerable wheel, such as bicycles, motor-bicycles, motorcycles or tricycles. To minimise the total mass of the unsprung suspension elements, by relocating the elastic and the damping elements to the springing side, the suspension contains at least one cable (10) connected at one end to the upper part of the front wheel fork (1), able to shift in relation to the fork column (6) of the handle bar (7), and at the other end to the elastic element (14) and/or the damping element (11), supported on at least one end by the vehicle frame (8), wherein the cable (10) goes through the handle bar (7) steering axis. The cable (10) is preferably led on at least one leading element (16) supported by the vehicle frame. Optionally, the cable (10) may be connected on the other end to the fork (18) of the vehicle rear suspension.