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A novel method is presented for echo-cancellation in long distance telephone connections. In contrast with conventional echo suppressors, the device described achieves echo-cancellation without interrupting the return path. A replica of the echo is synthesized and subtracted from the return signal. The replica is synthesized by means of a filter which, under the control of a feedback loop, adapts to the transmission characteristic of the echo path and tracks variations of the path that may occur during a conversation. The adaptive control loop is described by a set of simultaneous, nonlinear, first-order differential equations. It is shown that under ideal conditions, the echo converges to zero. Estimates of the rate of convergence are obtained. Effects of noise are discussed. The results of computer simulations of various alternative configurations of the system are described.