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Least-mean-square (LMS) and block LMS (BLMS) adaptive filters are generally believed to have similar step-size bounds for convergence. Similarly, convergence analyses of frequency-domain block LMS (FBLMS) adaptive filters have suggested that they have very restrictive convergence bounds. In this letter, we revisit Feuer's work and reveal a much larger convergence bound for BLMS adaptive filters. We then analyze the convergence properties of the FBLMS adaptive filter. The new step-size bound for the FBLMS adaptive filter, regardless of whether the input is white or colored, is not that restrictive as generally assumed for the block algorithms in the literature. Extensive simulation results are included to support the analyses.