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Two variable step-size normalized least mean square (VSS-NLMS) algorithms, namely the non-parametric VSS-NLMS and switched mode VSS-NLMS, are reformulated into complex signal form for STAP applications. The performances of these two VSS NLMS algorithms in Gaussian and compound-K clutters are evaluated via a phased array space-slow-time STAP example. We find that the misadjustment behaviors are inconsistent with the excess MSEs which is a better measure of STAP performance. Both VSS-NLMS algorithms outperform conventional fixed step-size (FSS) NLMS algorithms with fast convergence and low steady-state excess MSE. The SM-VSS-NLMS provides a better performance compromise than the NP-VSS-NLMS with much lower steady-state excess MSEs and slightly slower convergence speeds. The performance gain of both VSS algorithms reduces in heavy-tailed clutter environments than that in Gaussian clutters. Their robustness against impulsive interference is better than conventional FSS-NLMS.