1. A method of performing priority control for cells in an output buffer type ATM switch including a switching unit, having a plurality of input ports and a plurality of output ports, for switching/outputting the cells input from said input ports to said output ports in accordance with routing information, and a plurality of output buffer units having output buffer memories, connected to said output ports of said switching unit, for temporarily storing the cells output from said output ports to perform output control of the cells, comprising the steps of: adding a loss quality class, a delay quality class and the routing information to each of the cells; virtually setting a plurality of logical queues, for temporarily storing the cells, in input buffer memories in accordance with the delay quality classes and the routing information; selectively writing the input cells in said logical queues on the basis of the loss quality classes and the routing information added to the cells; performing a transition process for all said logical queues to change the delay quality class of each of said logical queues into one of upper and lower classes depending on a cell storage amount in said logical queue; and upon completion of the transition process, reading the cells from said logical queue having the delay quality class which is an uppermost class.