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We propose and experimentally demonstrate a nondestructive method to monitor chromatic dispersion (CD) and polarization-mode dispersion (PMD) in traffic-carrying wavelength-division-multiplexing optical systems. Coherent heterodyne detection is used to down convert the spectrum of digitally modulated signal from optical domain into radio-frequency (RF) domain. By analyzing group delay difference and polarization walkoff between different frequency components through proper RF signal processing, both CD and PMD can be precisely determined. Good agreement between experimental results and theoretical values has been obtained.