Abstract: A multiple access telecommunication system is provided, which makes use of chaotic signals. Each transmitter has a chaotic system, which has at least one strange attractor in its phase space, and each receiver has chaotic systems, which corresponds to those in the transmitters from which it may receive signals. Each pair of users is assigned a set of periodic unstable orbits from a strange attractor, which that pair of users may use for signalling. At the transmitter side, a multiplexer receives data from plurality of users. These data are multiplexed in time, to produce an asynchronous data stream. The data stream is then mapped to a sequence of chaotic signals, in accordance with the set of trajectories for each transmitter and receiver pair.