A hinge device for the controlled rotary opening and closing movement of a closing element anchored to a stationary support structure includes a fixed element and a movable element rotatable between a first open position and a closed position. The movable element includes an end portion, a working chamber, a shaft inserted therein, and a stem slidingly inserted into the shaft. A pin connects the end portion, the shaft, and the stem. The working chamber includes a working fluid for the hydraulic damping of the mutual movement of the fixed and movable elements and an elastic damping element causing the stem to abut thereagainst only when the stem is in an end-stop position, so that a user moving the closing element feels the resistance of the elastic damping element only upon reaching the first open position.