Summary: We study the propagation of capillary-gravity waves forced by a pressure distribution acting locally on the free surface and moving at constant velocity. The analysis is performed near the minimum velocity of dispersion curve. Near this velocity, the linearized Rayleigh theory is no longer valid, and one must include nonlinear terms. In order to do this, we use the theory developed by A. Mielke [J. Differ. Equations 65, 89-116 (1986; Zbl 0672.76017)] for the forced propagation of gravity waves near critical Froude number.