Motor-vehicle suspension system, comprising: - a suspension, - at least one transverse arm (T1, T2) for each wheel support, having one end pivotally connected to the respective wheel support and the opposite end pivotally connected to a motor-vehicle supporting structure, - a suspension spring which counteracts the vertical movements of the two wheel supports, consisting of a leaf spring arranged transversally with respect to the longitudinal direction of the motor-vehicle, with its general plane lying horizontally and connected to the motor-vehicle supporting structure by means of elastic supports arranged symmetrically at intermediate positions between the centre of the leaf spring and its ends, these ends of the leaf spring being pivotally connected to the two wheel supports at the upper part of each wheel support, and - two jack-type shock absorbers interposed between the wheel supports and the motor-vehicle supporting structure, wherein each jack-type shock absorber has its opposite ends swingably connected to the respective wheel support and the motor-vehicle supporting structure, characterized in that: - said suspension is a multi-link suspension, in which each wheel support is connected to the motor-vehicle supporting structure by means of two transverse lower arms (T1, T2) of said at least one transverse arm, a substantially longitudinal or inclined lower arm and at least one upper transverse arm constituted by the respective end portion of the leaf spring, in that said leaf spring comprises a single leaf in a one-piece construction, preferably of a composite material, which comprises two portions of enlarged thickness at said intermediate positions for connection to the respective elastic supports, each of said portions of enlarged thickness on its turn comprising two seats for two respective elastic supports connected to the motor-vehicle supporting structure, said seats being spaced apart from each other and aligned along the longitudinal direction of the motor-vehicle, each of said seats for the elastic supports of said leaf spring being defined by a vertical through aperture formed at each of said portions of enlarged thickness of the leaf spring, and in that said leaf spring has a width along the longitudinal direction of the motor-vehicle which has a maximum value at said intermediate portions of enlarged thickness and in that the end portions of the leaf spring which extend beyond said intermediate portions have a triangular configuration, with a base secured to the motor-vehicle supporting structure by means of said elastic supports and an apex at the end of the leaf spring, which is pivotally connected to the wheel support. - a suspension, - at least one transverse arm (T1, T2) for each wheel support, having one end pivotally connected to the respective wheel support and the opposite end pivotally connected to a motor-vehicle supporting structure, - a suspension spring which counteracts the vertical movements of the two wheel supports, consisting of a leaf spring arranged transversally with respect to the longitudinal direction of the motor-vehicle, with its general plane lying horizontally and connected to the motor-vehicle supporting structure by means of elastic supports arranged symmetrically at intermediate positions between the centre of the leaf spring and its ends, these ends of the leaf spring being pivotally connected to the two wheel supports at the upper part of each wheel support, and - two jack-type shock absorbers interposed between the wheel supports and the motor-vehicle supporting structure, wherein each jack-type shock absorber has its opposite ends swingably connected to the respective wheel support and the motor-vehicle supporting structure, characterized in that: - said suspension is a multi-link suspension, in which each wheel support is connected to the motor-vehicle supporting structure by means of two transverse lower arms (T1, T2) of said at least one transverse arm, a substantially longitudinal or inclined lower arm and at least one upper transverse arm constituted by the respective end portion of the leaf spring, in that said leaf spring comprises a single leaf in a one-piece construction, preferably of a composite material, which comprises two portions of enlarged thickness at said intermediate positions for connection to the respective elastic supports, each of said portions of enlarged thickness on its turn comprising two seats for two respective elastic supports connected to the motor-vehicle supporting structure, said seats being spaced apart from each other and aligned along the longitudinal direction of the motor-vehicle, each of said seats for the elastic supports of said leaf spring being defined by a vertical through aperture formed at each of said portions of enlarged thickness of the leaf spring, and in that said leaf spring has a width along the longitudinal direction of the motor-vehicle which has a maximum value at said intermediate portions of enlarged thickness and in that the end portions of the leaf spring which extend beyond said intermediate portions have a triangular configuration, with a base secured to the motor-vehicle supporting structure by means of said elastic supports and an apex at the end of the leaf spring, which is pivotally connected to the wheel support.