A packet switching system capable of ensuring the sequence and continuity of packets and further compensating for delays in transmission is disclosed. Each of two redundant switch sections has a high-priority queue and a low-priority queue for each of output ports. A high-priority output selector selects one of two high-priority queues corresponding to respective ones of the two switch sections to store an output of the selected one into a high-priority output queue. A low-priority output selector selects one of two low-priority queues corresponding to respective ones of the two switch sections to store an output of the selected one into a low-priority output queue. The high-priority and low-priority output selectors are controlled depending on a system switching signal and a packet storing status of each of the high-priority and low-priority queues.