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We present a kernel-based recursive least-squares (KRLS) algorithm on a fixed memory budget, capable of recursively learning a nonlinear mapping and tracking changes over time. In order to deal with the growing support inherent to online kernel methods, the proposed method uses a combined strategy of growing and pruning the support. In contrast to a previous sliding-window based technique, the presented algorithm does not prune the oldest data point in every time instant but it instead aims to prune the least significant data point. We also introduce a label update procedure to equip the algorithm with tracking capability. Simulations show that the proposed method obtains better performance than state-of-the-art kernel adaptive filtering techniques given similar memory requirements.