A lock having an alarm function for a two-wheeler, said lock comprising a lock body and a securing hoop which is movable relative to the lock body between a securing position to secure the two-wheeler and an open position to release the two-wheeler, wherein the lock body has a locking mechanism to selectively lock the securing hoop at the lock body in the securing position, and wherein the lock body further comprises an alarm device for outputting an alarm signal, wherein the locking mechanism can selectively be moved into an unlocked position, a locked position or an alarm activation position, wherein the securing hoop is released for a movement into the open position in the unlocked position, wherein the securing hoop located in the securing position is locked at the lock body and the alarm device is deactivated in the locked position, and wherein the alarm activation position forms a further locked position in which the securing hoop located in the securing position is locked at the lock body and the alarm device is activated, characterized in that the locking mechanism has a lock cylinder which is rotationally actuable by means of a key, with the lock cylinder having a cylinder housing and a cylinder core rotatably supported in the cylinder housing, with the locked position of the locking mechanism corresponding to a first rotational position of the cylinder core, with the alarm activation position of the locking mechanism corresponding to a second rotational positon of the cylinder core, and with the unlocked position of the locking mechanism corresponding to a third rotational position of the cylinder core, with the key being introducible into the cylinder core and removable from the cylinder core in the first rotational position of the cylinder core and in the second rotational position of the cylinder core. wherein the locking mechanism can selectively be moved into an unlocked position, a locked position or an alarm activation position, wherein the securing hoop is released for a movement into the open position in the unlocked position, wherein the securing hoop located in the securing position is locked at the lock body and the alarm device is deactivated in the locked position, and wherein the alarm activation position forms a further locked position in which the securing hoop located in the securing position is locked at the lock body and the alarm device is activated, characterized in that the locking mechanism has a lock cylinder which is rotationally actuable by means of a key, with the lock cylinder having a cylinder housing and a cylinder core rotatably supported in the cylinder housing, with the locked position of the locking mechanism corresponding to a first rotational position of the cylinder core, with the alarm activation position of the locking mechanism corresponding to a second rotational positon of the cylinder core, and with the unlocked position of the locking mechanism corresponding to a third rotational position of the cylinder core, with the key being introducible into the cylinder core and removable from the cylinder core in the first rotational position of the cylinder core and in the second rotational position of the cylinder core.