A packet relay system includes a first packet relay device and a second packet relay device. One of the first packet relay device and the second packet relay device relays a packet based on a first priority level of the first packet relay device and on a second priority level of the second packet relay device, the first priority level is higher than the second priority level, when the first packet relay device recovers from an error state, the first packet relay device transmits a first notification, the first notification notifies the second packet relay device of the first priority level, based on the first notification, the second packet relay device changes the second priority level to a third priority level that is higher than the first priority level, and the second packet relay device changes the third priority level to the second priority level after receiving path information.