In time-compression multiplex (t.c.m.) transmission, the signals of the channels are scanned and the samples are stored before being transmitted at high speed. In this way, the signals of a large number of channels can be sent over a single transmission path. Methods of time-compression multiplexing that are described include the use of a cathode-ray storage tube, a delay-line store and a gated-capacitor store. The function of the store is to change the order in which the samples of the channels occur in time. In the transmitted waveform, samples are arranged in groups. Each group comprises consecutive samples from a single channel and is separated by a short interval from the next group containing samples of another channel.It is shown that t.c.m. transmission requires less bandwidth than time-division multiplex transmission. As the time of storage is increased, the bandwidth required for t.c.m. decreases towards that for frequency-division multiplexing (f.d.m.). For storage times of the order of 10ms, the bandwidth needed for t.c.m. is little greater than that needed for f.d.m.It is shown that bandwidth limitation introduces attenuation distortion and a form of interference that is called grouping noise. However, this noise can be practically eliminated by transmitting redundant ‘guard’ samples before and after the group of signal samples of each channel. Another source of noise is store-switching noise. This can be eliminated by interweaving the scanning sequences of the stores.The feasibility of t.c.m. transmission was demonstrated by experiments on model systems using gated-capacitor stores. The development of practical t.c.m. systems depends on the availability of suitable stores. It appears that the cathode-ray storage tube may ultimately be the solution, but currently available tubes are inadequate.