Neural one-unit learning rules for the problem of Independent Com(cid:173) ponent Analysis (ICA) and blind source separation are introduced. In these new algorithms, every ICA neuron develops into a sepa(cid:173) rator that finds one of the independent components. The learning rules use very simple constrained Hebbianjanti-Hebbian learning in which decorrelating feedback may be added. To speed up the convergence of these stochastic gradient descent rules, a novel com(cid:173) putationally efficient fixed-point algorithm is introduced.