The stability of a two-dimensional vortex sheet against small disturbances in the plane of flow is examined. An integro-differential equation for the disturbances is derived and the possibility of solving it approximately is discussed. The approximation is equivalent to saying that short waves grow in a fashion determined by the local strength of the vortex sheet and it is shown that this need not be true throughout the evolution of the disturbance unless the growth rate is the same everywhere. It is possible for the disturbance on a distant part of the vortex sheet to control what happens locally, if the disturbance on the distant part is growing more rapidly. The approximate theory is applied to the tightly-wound spirals of aerodynamic interest and these are shown to be stable.