In an air-conditioning system, an outdoor unit and an indoor unit communicate through a relay device, including a plurality of communication ports; a plurality of communication networks having logical connection relationships with the respective communication ports; and a plurality of nodes having logical connection relationships with the respective communication networks. The plurality of nodes are each associated with one of the outdoor unit and the indoor unit. Among the plurality of nodes, a certain node is set as a first node, and another certain node different from the first node is set as a second node. The relay device executes transfer processing of transferring a communication frame from the first node to the second node, and then if the relay device does not receive a reception acknowledgment signal from the second node, limits a number of re-transmission times when the relay device re-transfers the communication frame to the second node.