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Estimating fixed directions-of-arrival of signals has generally been the objective in the literature. In this paper, however, we are concerned with time-varying directions-of-arrival. We propose here two different architectures of neural networks (feedforward and radial basis function networks) to estimate time-varying directions-of-arrival of signals. These networks are more amenable for hardware implementation compared to the conventional super-resolution techniques. The objective is to use these estimated directions to extract the signals. We demonstrate that neural networks of low complexity achieve our purpose, and the overall system sufficiently robust to account for the inaccuracies in the estimation of directions.