A rear-wheel suspension system for a two-wheeled vehicle includes a pair of right- and left-side center frames; a swing arm; and a shock absorber, wherein the shock absorber includes a tubular buffer and a spring, wherein the intake system part is a curved tubular member, wherein a position of the spring is shifted downwardly so that the intake system part are moved toward an interior of the vehicle body by a dimension corresponding to the spring, wherein a lower end of the intake system part is above the upper end of the spring, wherein a part of the intake system part is closer than an outer end of the spring to the center of the tubular buffer, and wherein the shock absorber and the intake system part are disposed between a pair of right- and left-side center frames.