A shock absorber system, comprising: a hydraulic shock absorber disposed between a sprung portion and an unsprung portion of a vehicle, the hydraulic shock absorber being configured to extend and contract in accordance with a relative movement of the sprung portion and the unsprung portion in an up-down direction and to generate a damping force with respect to the relative movement; a damping-force changer configured to give a resistance to a flow of a working fluid caused in the hydraulic shock absorber by the relative movement of the sprung portion and the unsprung portion and to change a magnitude of the resistance, so as to change the damping force to be generated by the hydraulic shock absorber; and a controller configured to determine a damping-force index that is an index for changing the damping force and to control the damping-force changer based on the determined damping-force index, so as to control the damping force to be generated by the hydraulic shock absorber, characterized in that the controller is configured to determine, as the damping-force index, a required application force (F *) that is a force to be applied to the sprung portion for damping a movement of the sprung portion in the up-down direction, according to a determination rule, in which the required application force has the same direction as a direction of a sprung speed (v) that is a speed of the sprung portion in the up-down direction when the sprung speed (v) is relatively small and sprung acceleration (α) that is acceleration of the sprung portion in the up-down direction is relatively large in a situation in which the direction of the sprung speed (v) and a direction of the sprung acceleration (α) are mutually different, wherein in a coordinate system whose transverse axis represents the sprung speed (v) and vertical axis represents the sprung acceleration (α), where there is set a boundary line, which passes an origin at which both of the sprung speed (v) and the sprung acceleration (α) are 0 and which extends across a second quadrant and a fourth quadrant, the determination rule is visually defined as: in the determination rule the required application force (F *) has the same direction as the direction of the sprung speed (v) when the sprung speed (v) and the sprung acceleration (α) belong to a region in the second quadrant that is located on one of opposite sides of the boundary line nearer to a first quadrant or a region in the fourth quadrant that is located on one of opposite sides of the boundary line nearer to a third quadrant. a hydraulic shock absorber disposed between a sprung portion and an unsprung portion of a vehicle, the hydraulic shock absorber being configured to extend and contract in accordance with a relative movement of the sprung portion and the unsprung portion in an up-down direction and to generate a damping force with respect to the relative movement; a damping-force changer configured to give a resistance to a flow of a working fluid caused in the hydraulic shock absorber by the relative movement of the sprung portion and the unsprung portion and to change a magnitude of the resistance, so as to change the damping force to be generated by the hydraulic shock absorber; and a controller configured to determine a damping-force index that is an index for changing the damping force and to control the damping-force changer based on the determined damping-force index, so as to control the damping force to be generated by the hydraulic shock absorber, characterized in that the controller is configured to determine, as the damping-force index, a required application force (F *) that is a force to be applied to the sprung portion for damping a movement of the sprung portion in the up-down direction, according to a determination rule, in which the required application force has the same direction as a direction of a sprung speed (v) that is a speed of the sprung portion in the up-down direction when the sprung speed (v) is relatively small and sprung acceleration (α) that is acceleration of the sprung portion in the up-down direction is relatively large in a situation in which the direction of the sprung speed (v) and a direction of the sprung acceleration (α) are mutually different, wherein in a coordinate system whose transverse axis represents the sprung speed (v) and vertical axis represents the sprung acceleration (α), where there is set a boundary line, which passes an origin at which both of the sprung speed (v) and the sprung acceleration (α) are 0 and which extends across a second quadrant and a fourth quadrant, the determination rule is visually defined as: in the determination rule the required application force (F *) has the same direction as the direction of the sprung speed (v) when the sprung speed (v) and the sprung acceleration (α) belong to a region in the second quadrant that is located on one of opposite sides of the boundary line nearer to a first quadrant or a region in the fourth quadrant that is located on one of opposite sides of the boundary line nearer to a third quadrant.