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The inviscid instability of Stokes layers is investigated. The Stokes layer is shown to support inviscid Floquet modes at sufficiently high values of the disturbance wavenumbers. Other non-Floquet modes are investigated and are shown to be the likely cause for instability in Stokes layers. These modes intersect with a viscous continuous spectrum of disturbances and it is this interaction which enables free-stream disturbances to penetrate into the boundary layer and amplify exponentially. The relevance of the inviscid theory to previous viscous instability calculations for Stokes layers is discussed.