A suspension system for vehicles with at least two wheels comprising a rigid structure supporting the axle of a rear wheel of the vehicle and a damping device , the rigid structure comprising a lower arm and an upper arm angled and connected to corresponding upper and lower points of the chassis of the vehicle through corresponding lower mechanism and upper mechanism , respectively, that provide movement, in a guided way and under the influence of the damping device , of the rigid structure with regard to the chassis , of which: - the lower mechanism comprises a lower connecting rod having articulated joints with the lower arm of the rigid structure and the chassis that are at least 20 mm apart from one another, the articulated joint with said lower arm of the rigid structure being arranged, in the forward direction of the vehicle, ahead of or matching the vertical plane passing through the output axle of the driving mechanism of the vehicle - the bottom bracket in the case of a bicycle - - the upper mechanism comprising an upper connecting rod having articulated joints with the upper arm of the rigid structure and chassis, the articulated joint with the chassis being arranged, in the forward direction of the vehicle, ahead of or matching the vertical plane passing through the articulated joint of the lower connecting rod with the chassis, - at least one of the upper or lower connecting rods (7; 8) forming part of a lever (9; 10) whose fulcrum (f; f') is the articulated joint of the connecting rod with the chassis and whose resistance is an articulated joint (9a or 10a) with one of the ends (6a or 6b) of the damping device , the suspension system being characterized in that the arrangement and orientation of the lower and upper connecting rods (7 or 8) is such that the Instant Rotation Center (IRC) of the rigid rigid structure remains, during the whole work stroke of the damping device , ahead of the articulated joint of the lower connecting rod with the chassis , and in that the lower connecting rod is used as the support of a sprocket or pulley that, acting as a loose pulley, is intended to support and offset a transmission chain or belt . - the lower mechanism comprises a lower connecting rod having articulated joints with the lower arm of the rigid structure and the chassis that are at least 20 mm apart from one another, the articulated joint with said lower arm of the rigid structure being arranged, in the forward direction of the vehicle, ahead of or matching the vertical plane passing through the output axle of the driving mechanism of the vehicle - the bottom bracket in the case of a bicycle - - the upper mechanism comprising an upper connecting rod having articulated joints with the upper arm of the rigid structure and chassis, the articulated joint with the chassis being arranged, in the forward direction of the vehicle, ahead of or matching the vertical plane passing through the articulated joint of the lower connecting rod with the chassis, - at least one of the upper or lower connecting rods (7; 8) forming part of a lever (9; 10) whose fulcrum (f; f') is the articulated joint of the connecting rod with the chassis and whose resistance is an articulated joint (9a or 10a) with one of the ends (6a or 6b) of the damping device , the suspension system being characterized in that the arrangement and orientation of the lower and upper connecting rods (7 or 8) is such that the Instant Rotation Center (IRC) of the rigid rigid structure remains, during the whole work stroke of the damping device , ahead of the articulated joint of the lower connecting rod with the chassis , and in that the lower connecting rod is used as the support of a sprocket or pulley that, acting as a loose pulley, is intended to support and offset a transmission chain or belt . <EOS>