The lid for a rear trunk of a vehicle having a roof foldable into the trunk is connected to the bodywork by device disposed at the front edge and at the rear edge of the lid and whose function is either to lock or to hinge the lid in a manner such that said lid can open either from the front backwards or from the rear forwards, and control device cause the lid to open in either of its opening directions or to be closed. According to the invention, the control device comprise at least one articulated arm and an actuator which is connected to the articulated arm and to the bodywork, and which is adapted to move the articulated arm and the lid.