The present invention is directed to an echo canceller adapted for use in a communication system that includes a hybrid circuit. The echo canceller comprises an adaptive digital filter that generates an estimated echo signal {circumflex over (z)}[k] in response to: (i) a sampled input data sequence x[k] and (ii) an error signal sequence e[k] indicative of the difference between a near end signal sequence y[k] and the estimated echo signal {circumflex over (z)}[k]. The adaptive digital filter computes filter coefficients based upon the error signal sequence e[k] using a stochastic quadratic descent estimator, such as for example a least mean square (LMS) estimator, that employs a dynamically adjustable step size vector [k]. The adaptive digital filter computes the dynamically adjustable step size vector [k] of the form ##EQU1##

where [k+1]=[k](1-[k]x²[k])+e[k])+e[k]x[k] and is a scalar. In an open loop embodiment, the dynamically adjustable step size vector [k] equals to [k]=[k]1, that is, all elements of the vector take the same value collapsing to the particular case of a scalar. The step size is computed using an expression of the form [k+1]=[k]+[k], where [k] is an empirically derived set of values.