Abstract: A pulse stuffing multiplexer apparatus is used in order to carry out multiplexing of these signals. The low order data signal for a single channel is stored into an m-bit memory in accordance with a clock signal obtained by demultiplying the low order clock signal of that channel to l/m to be read out as the high order data signal by a clock signal obtained by demultiplying a common high order clock signal not lower than all the low order clock signals to l/m. When the high order data signal is read out from this memory, an S-th (S.ltoreq.m) of both clock signals is monitored and, when the phase difference therebetween falls within predetermined k-bits (k.ltoreq.m), both demultipliers are reset at the head position of the next frame for both clock signals to be initialized at a predetermined position.