a digital signal multiplexing apparatus comprising variable multiplexers each of which can alter a multiplexed channel format every call in compliance with a subscriber &# 39 ; s request , a fixed multiplexer which has a multiplexing capacity integral times as large as the total multiplexing capacity of the variable multiplexers and the multiplexed channel format of which is fixed , and fixed multiplexed signal demultiplexers each of which fixedly demultiplexes signals in a capacity integral times as large as that of each of the variable multiplexers into signals in a capacity equal to the total capacity of the variable multiplexers , wherein the outputs of the fixed multiplexed signal demultiplexers are distributed to the variable multiplexers through a distributing switch network , and the outputs of the variable multiplexers are multiplexed by the fixed multiplexer .