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Optical fiber microwires (OFMs) are nonlinear optical waveguides that support several spatial modes. The multimodal generalized nonlinear Schrödinger equation (MM-GNLSE) is deduced taking into account the linear and nonlinear modal coupling. A detailed theoretical description of four-wave mixing (FWM) considering the modal coupling is developed. Both, the intramode and the intermode phase-matching conditions is calculated for an optical microwire in a strong guiding regime. Finally, the FWM dynamics is studied and the amplitude evolution of the pump beams, the signal and the idler are analyzed.