A hinge device of a nacelle cowling of an aircraft engine on a supporting structure is disclosed. The hinge device includes two fittings and a link rod connected thereto and mounted on the fitting by an end connection. The link rod is further mounted on the fitting by an intermediate connection including a pivot pin slidably housed in a hole, and the end connection includes a guide pin slidably housed in a guide ramp. The connections are designed so as to create, upon rotation of the link rod about the pin, a relative movement of the axis in the ramp, simultaneously causing a relative movement of the pin in the hole.