A frame for bicycle provided with a rear suspension system, comprising: a front triangle having a vertical tube, or seatstay, , an upper oblique tube , and a lower oblique tube ; a rear triangle having a pair of lower tubes and a pair of high tubes , the rear triangle being pivotably connected to the front triangle in order to allow a movement of the axis of rotation (x) of the rear wheel of the bicycle along a given trajectory with respect to the front triangle ; a movable element which is carried by the front triangle which the high tubes are operatively hinged to in correspondence of their upper ends around a hinging axis (x 3 ), said movable element being a rod-like element; and a rear damper connected to said movable element in such a way as to exert on the latter a damping force tending to reduce the oscillations of the rear triangle in comparison with the front triangle ; being also provided guiding means suitable for guiding said movable element in a sliding manner with respect to the front triangle along an axis of movement (s) which is fixed with respect to the front triangle , characterized in that said guiding means comprise at least two support bodies , housed inside a tube and transversally secured to said tube of the front triangle , having respective guiding holes aligned to each other so as to define said axis of movement (s), the movable element arranged in said guiding holes sliding within said guiding holes in a guided manner, said tube wherein are placed and secured the guiding means being part of the front triangle or being secured thereto, a support structure forming the support bodies , said support structure being secured to the corresponding tube . a front triangle having a vertical tube, or seatstay, , an upper oblique tube , and a lower oblique tube ; a rear triangle having a pair of lower tubes and a pair of high tubes , the rear triangle being pivotably connected to the front triangle in order to allow a movement of the axis of rotation (x) of the rear wheel of the bicycle along a given trajectory with respect to the front triangle ; a movable element which is carried by the front triangle which the high tubes are operatively hinged to in correspondence of their upper ends around a hinging axis (x 3 ), said movable element being a rod-like element; and a rear damper connected to said movable element in such a way as to exert on the latter a damping force tending to reduce the oscillations of the rear triangle in comparison with the front triangle ; being also provided guiding means suitable for guiding said movable element in a sliding manner with respect to the front triangle along an axis of movement (s) which is fixed with respect to the front triangle , characterized in that said guiding means comprise at least two support bodies , housed inside a tube and transversally secured to said tube of the front triangle , having respective guiding holes aligned to each other so as to define said axis of movement (s), the movable element arranged in said guiding holes sliding within said guiding holes in a guided manner, said tube wherein are placed and secured the guiding means being part of the front triangle or being secured thereto, a support structure forming the support bodies , said support structure being secured to the corresponding tube . <EOS>