Locking device for movable furniture parts

A locking device for movable furniture parts has a guide rail with displaceable blocking elements, a plurality of latches that can be coupled to a movable furniture part, and, in a locking position, block an opening of the movable furniture part. The blocking elements are movable into a locking position in which all the latches are blocked by the blocking elements from a movement into an unlocking position, and the blocking elements are displaceable along the guide rail in an anti-tipping position via one of the latches, from the locking position into the unlocking position. When one of the latches is positioned in the unlocking position, the movement of all further latches into the unlocking position is blocked, so that only one of the movable furniture parts is moveable into an opening position.