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In this paper, we investigate for the first time chromatic dispersion and nonlinearity tolerances in the presence of polarization-mode dispersion (PMD) for polarization-multiplexed (POLMUX) 2 × 10-Gb/s nonreturn-to-zero (NRZ) transmission. In polarization-multiplexing, the interaction between fiber nonlinearity and PMD can lower the nonlinear tolerance beyond the tolerances evident when considering both transmission penalties separately; the combined penalties are significantly worse than in the case for non-POLMUX transmission. In this paper, we show, through simulations comparing POLMUX with non-POMUX transmission in the presence of nonlinearity, a reduction of about a factor of three in PMD tolerance. In addition, we show that the dispersion tolerance of POLMUX transmission is severely limited in the presence of PMD. For example, a 40-ps differential group delay (DGD) with worst case coupling of the polarization channels into the fiber lowers the dispersion tolerance, resulting in a 1-dB eye-opening penalty (EOP), from 1200 to 450 ps/nm. We conclude that the interaction between PMD, chromatic dispersion, and nonlinearity leads to the worst signal impairments in POLMUX transmission and increases the effort of using polarization-multiplexing as a modulation format.