This paper presents a novel approach to weight adaptation of single-layer perceptron (SLP) bused communication channel equalisers, by developing the Least-Mean-Absolute-Error adaptive algorithm using the absolute-error cost function. Theoretical and experimental results are provided and comparisons made between the present algorithm and the traditional back-propagation, Rosenblatt and linear LMS algorithms. This work shows that the proposed algorithm is faster in adapting the weights of the SLP-based equalisers and leads to better estimation performance.