| A neural-network controller operating in discrete time is shown to result in stable trajectory tracking for rigid and elastic-joint robots. The technique assumes continuous-time state feedback. The proof of stability uses discrete-time Lyapunov functions. For the elastic-joint case, a discrete-time version of the adaptive backstepping technique is used. The result is that the neural network can be run at a very slow control rate, suitable for online calculations. The neural network used is referred to as the CMAC-RBF Associative Memory (CRAM), a modification of Albus's Cerebellar Model Arithmetic Computer (CMAC) algorithm using radial basis functions (RBFs). Simulation results are provided for a two-link planar elastic-joint robot and show that performance can be improved by using a larger network at a slower control rate.