A hinge for the controlled rotatable movement of at least one closing element, such as a door, a shutter or the like, anchored to a stationary support structure, such as a wall, a floor, a frame or the like, the hinge comprising: - a pivot defining a first axis anchorable to one of said at least one closing element and said stationary supporting structure, said pivot comprising cam means; - a hinge body anchorable to the other of said at least one closing element and said stationary supporting structure, said hinge body and said pivot being rotatably coupled to rotate one with respect to the other around said first axis; - at least one hydraulic damping means comprising: - a jacket defining a second axis; - a plunger element comprising a first and a second end (32', 32"); wherein said hinge body comprises a working chamber defining a third axis ( Y') substantially perpendicular to said first axis comprising elastic counteracting means; wherein the at least one hydraulic damping means is configured as a hydraulic damping cylinder, said jacket being divided into at least one first and one second variable volume compartment (31', 31") placed in fluid communication with each other, said first and second ends (32', 32") of said plunger element being respectively inserted into said at least one first and one second variable volume compartments (31', 31") to slide sealingly integrally joined in said jacket; and wherein the hinge comprises a working fluid entirely contained in said jacket, said elastic counteracting means and said pivot remaining dry; and further said at least one hydraulic damping cylinder is removably mutually couplable with said pivot and with said hinge body so that: - said second and third axis ( Y, Y') coincide or are parallel to each other; - said elastic counteracting means interact with one of said first and second ends of said plunger element (32"), the other of said first and second ends of said plunger element being integrally coupled with cam follower means (32") susceptible to mutually interact with said cam means for displacing the at least one closing element between the at least one open position and at least one closed position. - a pivot defining a first axis anchorable to one of said at least one closing element and said stationary supporting structure, said pivot comprising cam means; - a hinge body anchorable to the other of said at least one closing element and said stationary supporting structure, said hinge body and said pivot being rotatably coupled to rotate one with respect to the other around said first axis; - at least one hydraulic damping means comprising: - a jacket defining a second axis; - a plunger element comprising a first and a second end (32', 32"); - a jacket defining a second axis; - a plunger element comprising a first and a second end (32', 32"); wherein said hinge body comprises a working chamber defining a third axis ( Y') substantially perpendicular to said first axis comprising elastic counteracting means; wherein the at least one hydraulic damping means is configured as a hydraulic damping cylinder, said jacket being divided into at least one first and one second variable volume compartment (31', 31") placed in fluid communication with each other, said first and second ends (32', 32") of said plunger element being respectively inserted into said at least one first and one second variable volume compartments (31', 31") to slide sealingly integrally joined in said jacket; and wherein the hinge comprises a working fluid entirely contained in said jacket, said elastic counteracting means and said pivot remaining dry; and further said at least one hydraulic damping cylinder is removably mutually couplable with said pivot and with said hinge body so that: - said second and third axis ( Y, Y') coincide or are parallel to each other; - said elastic counteracting means interact with one of said first and second ends of said plunger element (32"), the other of said first and second ends of said plunger element being integrally coupled with cam follower means (32") susceptible to mutually interact with said cam means for displacing the at least one closing element between the at least one open position and at least one closed position. - said second and third axis ( Y, Y') coincide or are parallel to each other; - said elastic counteracting means interact with one of said first and second ends of said plunger element (32"), the other of said first and second ends of said plunger element being integrally coupled with cam follower means (32") susceptible to mutually interact with said cam means for displacing the at least one closing element between the at least one open position and at least one closed position.