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A plane wave is incident upon a cylindrical surface comprised of two parabolic sections with different curvature at their junction but otherwise smoothly joined, such that the direction of their normals is continuous. The Neumann boundary condition is considered and an asymptotic expansion is obtained for the field on the surface. It is shown that the discontinuity will launch creeping waves on a curved surface, and the actual form of these waves are obtained. The special case where one of the curved surfaces degenerates into a plane is also considered.