There is disclosed a wristwatch (1) whose wristband (6) is attached to a support (3) with respect to which the case (2) can turn over to show one or other of its faces (16, 17). The support (3) includes, on the parallel inner surfaces (9) of its flanges (7), grooves (10) in which snugs (39) connected to the case can slide and pivot. Stops are provided in the grooves (10), to stop the case sliding after a first sliding travel of the snugs (39) from the ends (42) of the grooves, to define a pivoting zone of the case, before the snugs effect a second sliding travel to the other ends (42). Support surfaces (11) and a transverse recess (12) are provided on the bottom (4) of the support to prevent the case turning over except in the zone of the stops.