Abstract: An adaptive echo suppressor is provided at each local station in a data transmission system for transmission of local data from a local station to a remote station over a transmission medium exhibiting an echo and simultaneous transmission of far end data over said medium from said remote station. The echo suppressor comprises an adaptive echo suppressor located at said local station and comprising: an adaptive digital filter connected to receive the local data a.sub.x and a clean signal e.sub.k substantially free of echo and arranged to deliver on an output an estimation o.sub.k of the echo of the local data by multiplying a vector of coefficients C.sub.k with the local data a.sub.k, said vector having an adaptation algorithm:C.sub.k+1 =C.sub.k +.mu.a.sub.k *.multidot.f(e.sub.k)wherein .mu. is a predetermined incrementation step, a.sub.k * is a conjugated value of the local data a.sub.k, and f is a predetermined function of e.sub.