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Adaptive beamforming algorithms typically rely on a complex linear model between the sensor measurements and the desired signal output that does not enable the best performance from the data in some situations. In this paper, we present an extension of the well-known recursive least-squares algorithm for adaptive filters to widely-linear complex-valued signal and system modeling. The widely-linear RLS algorithm exploits a structured covariance matrix update that maintains information about the non-circularity of the input data to solve the widely-linear least-squares task at each snapshot. In addition, the WL-RLS algorithm can easily be switched between conventional and widely-linear complex modeling as needed. Application of the method to adaptive beamforming of mixed BPSK and QPSK signal transmissions shows that the system can extract all of the transmitted signal outputs in certain overloaded scenarios, and it performs up to 3dB better than the conventional RLS beamformer when the array is not overloaded.