A closure sequence controller for a double door arrangement in which the double door arrangement is provided with a first door closer and a first pull arm for closing a first door leaf and with a second door closer and a second pull arm for closing a second door leaf. A guide rail guides the distal ends of the pull arms relative to the door closers. The closure sequence controller includes a connection piece for transmitting a pulling force from the distal end of the first pull arm to the closure sequence controller. The closure sequence controller prevents movement of the distal end of the second pull arm in the guide rail past the closure sequence controller until the distal end of the first pull arm has exerted the pulling force on the closure sequence controller through the connection piece.