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We investigate both theoretically and experimentally the impact of pump-phase modulation on differential phase shift keying (DPSK) and differential quadrature phase shift keying (DQPSK) signals in fiber-based parametric wavelength converters. It will be shown that the pump-phase modulation used to suppress stimulated Brillouin scattering introduces critical signal degradations and optical SNR penalties on DPSK signals, and more severe on DQPSK signals. Different modulation schemes will be theoretically investigated and the quantitative results are compared to system experiments. Finally, the theoretical results for a single conversion will be extended to multiple conversions to study the cascadability of the wavelength converter.