A motor-vehicle multi-link suspension system includes, for each wheel, two lower transverse arms and a substantially longitudinal or inclined lower arm, each having one end pivotally connected to a respective wheel support and the opposite end pivotally connected to the motor-vehicle structure. A leaf spring is arranged transversally with respect to the longitudinal direction of the motor-vehicle. The leaf spring is supported by elastic supports arranged symmetrically at intermediate positions between the center of the leaf spring and the ends thereof. Ends of the leaf spring are pivotally connected to upper parts of the two wheel supports. Two jack-type shock absorbers have opposite ends swingably connected to the respective wheel support and the motor-vehicle structure. The end portions of the leaf spring also fulfill the function of triangular upper transverse arms of the multi-link suspension. Preferably the leaf spring is made of a composite material.