The authors present new learning algorithm schemes using feedback error learning for a neural network model applied to adaptive nonlinear control of a robot arm, namely the QR-WRLS algorithm and its parallel counterpart algorithms. It involves a QR decomposition to transform the system into upper triangular form, and estimation of the neural network weights by a weighted recursive least squares (WRLS) technique. The QR decomposition method, which is known to be numerically stable, is exploited in an algorithm which involves successive applications of a unitary transformation (Givens rotation) directly to the data matrix. The WRLS weight estimation method chosen allows the selection of weighting factors such that each of the linear equations is weighted differently. The QR-WRLS algorithm is shown to provide fast, robust and stable online learning of the dynamic relations necessary for robot control. We show the results of applying these learning schemes with some flexible forgetting strategies to a two-link manipulator. A comparison of their performance with backpropagation (BP) algorithm and the recursive prediction error learning algorithm is included (RPE).