A hinge (10) for mounting a door (14) on a piece of furniture, comprising a hinge arm (12) fixable to a fixed part (11) of the piece of furniture and a box (13) fixable to a door (14) of the piece of furniture, swingably connected to each other; the hinge further comprises a linear-type decelerating device (22) arranged inside the box (13), having a fluid-type decelerating cylinder (23) and return spring means (24), operatively connected with each other, which extend parallel to and spaced apart from each other. The fluid-type decelerating cylinder (23) is arranged in proximity to a side wall (18′) of the box (13) and the return spring means (24) are arranged in proximity to the opposite aide wall (18″) of the box (13).