A console (1) of a tunnel (2) for the passenger compartment of a vehicle has an outer structure (5) that houses, in a fixed position, a glove compartment (10) fitted with a hatch; the console (1) has a wall (24,24c), which is positioned outside of said compartment (10) and is movable, in response to an action by the user, with respect to an upper surface (8) of the structure (5), between a lowered position and a raised position, so as to project upwards with respect to this upper surface (8) and define an outer compartment (25) when located in the raised position.