Singularities encountered in solutions of the thin-shear-layer (boundary-layer) equations are examined. The point of zero surface shear stress is distinguished from points at which the rate of growth of shear layer thickness becomes large, which may be termed points of separation, but which do not represent mathematical singularities if the rate of growth is not infinite. A singularity has also been observed to occur above a point on the axis of the flow over a rotating disk in a counterrotating fluid. The Goldstein (1948) square root singularity, in which surface shear stress approaches zero, is shown to occur only in steady or quasi-steady flows. All singularities discovered thus far can be attributed to the failure of the shear layer calculations to conserve V-component momentum.