We introduce a computationally efficient frequency-domain implementation of a fractionally spaced block-least-mean-square (LMS) or block-constant-modulus-algorithm (CMA) equalizer. The proposed implementation is less complex than its time-domain counterpart. Besides, it lends itself naturally to high-throughput parallel architectures thanks to block-processing based on fast Fourier transforms. The resulting equalizer may be used for adaptive polarization-mode dispersion (PMD) equalization, or for joint adaptive compensation of chromatic dispersion (CD) and PMD in digital coherent receivers.