The invention discloses a cell order maintaining method and a cell order maintaining device, which divide unicast cell channels and multicast cell channels effectively under a unitcast and multicast mixing condition. The invention adopts a technical scheme which comprises that: firstly, a source switching access chip makes a global time stamp on cells, which are about to dequeue, according to the respective attribute values of unicast cells and multicast cells as well as makes multicast time stamps on the unicast cells while making time stamps on the unicast cells in order to a basis for the generation of unicast idle cells of a downstream switching chip and makes unicast time stamps on the multicast cells while making time stamps on the multicast cells in order to provide a basis for the generation of the unicast cells of the downstream switching chip; secondly, the switching chip compares the unicast cells with the multicast cells according to the global time stamps and outputs the oldest cells to a subordinate switching chip, and the last switching chip transmit the cells to different input queues in a target switching access chip; and thirdly, the target exchange chip selects and outputs the cells with the earliest time stamps in each link to realize the functions of the entire switching network.