The existence of a critical value of the Stokes number, St,, below which no particle impaction takes place, has been demonstrated for inviscid stagnation flows in the absence of sedimentation. In the inviscid approximation, St, is inversely proportional to the normal gradient of the inward velocity at the stagnation point. In practice, the effect of viscosity is to increase the value of St,, because the convective how velocity towards the surface is reduced. Using asymptotic matching techniques, we calculate approximately the increase in St, for large-Reynolds-number stagnation flows, either two-dimensional or axisymmetric, for which there is a thin viscous boundary layer near the surface. Numerical calculations for unseparated flow around spheres and cylinders show that the increase owing to viscosity is likely to be significant under all laminar flow conditions, even though the viscous boundary layer may be very thin. The sensitivity to the shape of the body on which the particles are deposited, and the likely effects of flow separation, are briefly discussed.