The response of a wall boundary layer to the motion of a convected vortex is investigated. The principal cases considered are for a rectilinear filament of strength βΞΊ located a distance a above a plane wall and convected to the right in a uniform flow of speed Uβ. The inviscid solution predicts that such a vortex will remain at constant height a above the wall and be convected with constant speed Ξ±Uβ. Here Ξ± is termed the fractional convection rate of the vortex, and cases in the parameter range 0 [les ] Ξ± < 1 are considered. The motion is initiated at time t* = 0 and numerical calculations of the developing boundary-layer flow are carried out for Ξ± = 0, 0.2, 0.4, 0.55, 0.7, 0.75 and 0.8. For Ξ± < 0.75, a rapid lift-up of the boundary-layer streamlines and strong boundary-layer growth occurs in the region behind the vortex; in addition an unusual separation phenomenon is observed for Ξ± [les ] 0.55. For Ξ± [ges ] 0.75, the boundary-layer development is more gradual, but ultimately substantial localized boundary-layer growth also occurs. In all cases, it is argued that a strong inviscidβviscous interaction will take place in the form of an eruption of the boundary-layer flow. The generalization of these results to two-dimensional vortices with cores of finite dimension is discussed.