Adaptive beamforming is used to enhance the detection of target echoes received by high frequency (HF) surface wave (HFSW) over-the-horizon (OTH) radars in the presence of spatially structured interference. External interference from natural and man-made sources typically masks the entire range-Doppler search space and is characterized by a spatial covariance matrix that is time-varying or nonstationary over the coherent processing interval (CPI). Adaptive beamformers that update the spatial filtering weight vector within the CPI are likely to suppress such interference most effectively, but the intra-CPI antenna pattern fluctuations result in temporal decorrelation of the clutter which severely degrades subclutter visibility after Doppler processing. A robust adaptive beamformer that effectively suppresses spatially nonstationary interference without degrading subclutter visibility is proposed here. The proposed algorithm is computationally efficient and suitable for practical implementation. Its operational performance is evaluated using experimental data recorded by the Iluka HFSW OTH radar, located near Darwin in far north Australia.