An echo cancelling device for use between a line receiving an incoming signal and a line transmitting an outgoing signal, for cancelling out echo, comprising a plurality of processing channels connected in parallel relation and assigned to successive mutually adjacent sub-bands of the spectral band of the outgoing signal, each channel having: a first analysis band-pass filter receiving the echo-affected signal to be transmitted, whose output is connected to the additive input of a subtractor; a second analysis band-pass filter, identical to the first filter, receiving the incoming signal and feeding an adaptive filter delivering an estimated echo value in the sub-band to the subtractive input of the subtractor; and a synthesis filter, symmetrical with the analysis filters and whose output feeds the transmission line. Each processing channel receives an estimation of the aliasing component originating from another sub-band at least and that component is eliminated by adding it to the signal originating from the filter analyzing the respective incoming signal. Estimation may be made by synthesis using at least one adaptive cross-filter fed by the output of an adjacent channel.