In a packet relay apparatus or bandwidth policing apparatus, when the bandwidth of a flow having a function to respond to a congestion notification surpasses a first threshold, a congestion notification is given to rewrite a value representing the congestion state of the network out of the packet headers of the packet received by the apparatus. The packet is dropped if the bandwidth of the flow surpasses a second threshold higher than the first threshold. One of the following, including packet drop, rewriting the value representing the priority level in the network out of the packet headers and altering the priority level in the apparatus is imposed on the packet when the bandwidth of the flows surpasses a second threshold higher than the first threshold.