Abstract: The sleeve for an electric cable comprises two bodies (2, 3) and a hinge (4). Each body (2, 3) is flexible in the profile thereof, has, in the absence of mechanical stress, a position of rest in which it is curved whereas it is designed for being bent from the position of rest. The sleeve has an open position in which the bodies (2, 3) are separated from one another when in the position of rest, has a first stable closed position in which a first body (3) receives the second body (2) and has a second stable closed position in which the second body (2) receives the first body (3). The sleeve is designed for being deformed by folding the hinge (4) and to flex in the profile of these bodies (2, 3) in order to pass from the open position into one or other said stable closed positions.