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The present work is a generalization of that dealing with a pair of knife-edges. In particular, a high-frequency solution is obtained for the scattering in the near zone of a pair of coplanar skew wedges with arbitrary exterior angle, illuminated by a source at finite distance. The solution is achieved by using a spherical wave spectral representation of the incident, singly diffracted field by the first wedge. The electromagnetic solution is constructed from the relevant scalar formulation by choosing appropriate ray-fixed reference systems. The final dyadic closed form expression is cast in the uniform theory of diffraction (UTD) framework, and includes terms up to the second order. These latter become of the same order as the leading terms in overlapping transition regions of the two wedges. This solution is also directly applicable when the two wedges share a common face for both polarizations; in this case, the second order terms provide an accurate description of those contributions that are usually neglected for soft polarization.