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We predict that a three-wave resonant interaction (TWRI) for the excitations created from a continuous-wave background is possible in nonlinear optical fibres with a centro-symmetry. We show that in normal dispersion regime and near the zero-dispersion point of a single-mode optical fibre, the phase-matching condition for the TWRI can be satisfied by suitably choosing the wavevectors and frequencies of the exciting waves. The nonlinear envelope equations for the TWRI are derived by using a method of multiple-scales, and their explicit solutions for sum- and difference-frequency mixing are provided and discussed.