clockwise see fig5 a when the upward load applied to the rear wheel is released and the rear fork 3 is swung downwardly by the force of the suspension spring 15 the damper 8 then expands and the first link 122 is turned downwardly to rotate the adjusting member 118 counterclockwise see fig5 therefore the damping force is generated by the expansion damping force generating device 16 and the damping force increases as the downward swinging amount of the rear fork 3 increases accordingly the downward swinging velocity of the rear fork 3 is more strongly restricted as the swinging amount thereof increases whereby a great swinging energy of the rear fork 3 may be effectively absorbed without being accompanied by a great shock within the range of a predetermined swinging stroke of the rear fork 3 fig6 shows a fourth embodiment of the present invention in which as the upward swinging amount of the rear fork 3 increases the contacting amount of the damper 8 increases in an accelerating manner more specifically to the rear fork 3 is connected via pivot 132 the rear end of a link 30 at an intermediate portion of the fork 3 for up and down swing motion front end of a tension rod 131 is pivoted at 133 to the body.