A device for blocking the pull-out movement of pull-out furniture parts including, for each of the pull-out furniture parts, a driver, a blocking unit which has a shiftable actuating, and a retraction spring and blocking rods which cooperate with the actuating parts, a respective actuating part that is shifted due to movement of the driver when the pull-out furniture part is pulled out and that displaces a blocking rod in a longitudinal axis direction, the blocking rods being blocked from any further axial displacement by a stop. Each of the blocking units has a pivotable catch arm that swivelable about a stationary pivot axis lying parallel to the longitudinal axes of the blocking rods and is loaded by the refraction spring, the catch arm being pivoted by the driver from an initial position to a final position when the pull-out furniture part is pulled out, thereby shifting the actuating part.