The dynamics of the mixed layer in the presence of an embedded geostrophic jet has been investigated using a simple 1½-layer model and a two-dimensional primitive equation model. The jet vorticity induces a spatial variability of the wind-driven inertial motions that can have some important consequences on the mixed-layer dynamics. With a steady wind stress parallel to the front, the main effect is the generation of steady upwellings and downwellings due to the divergence of the mean Ekman drift (as reported by Niiler). With a cross-front wind, however, a dramatic exponential amplification of the inertial oscillations caused by an inertial resonance mechanism is found: this mechanism can increase the inertial waves amplitude by a factor up to 10 within ten inertial periods. Competition between this resonance mechanism and the dispersion mechanisms (mainly the horizontal and vertical propagation of inertial waves) that can limit its effects has been assessed. A consequence of horizontal propagation is that energetic waves can propagate well away from the jet while continuing to absorb energy from the wind. Downward propagation disperses this energy to a depth of at least 500 m in a few days.