A gradient descent based on-line algorithm for blind source extraction (BSE) of instantaneous signal mixtures is proposed. This algorithm is derived by utilising a nonlinear adaptive filter in a structure that consists of an extraction and prediction module. By exploiting the predictability property of a signal from the mixture, source signals are extracted based on the order of the nonlinear adaptive predictor. To improve the convergence of the basic algorithm, it is further globally normalised based o n t h e minimisation of the a posteriori prediction error. Next, the algorithm is made fully adaptive to compensate for the independence and other assumptions in its derivation. Two examples are presented to illustrate the performance of the algorithms.