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We investigate oblique diffraction of arbitrarily polarized waves by axially slotted, dielectric-filled, perfectly conducting circular cylinders with infinitesimally thin walls. The relevant 2 × 2 system of coupled singular integral-integrodifferential equations is solved by a highly accurate Nyström method. For enhanced efficiency, several asymptotic terms are extracted from the kernels. This helps isolate the inherent singularities and, thus, transform the initial slowly converging Green-function expansions into rapidly converging series. As a consequence, all elements of the resulting Nyström matrix take exact expressions in the form of very rapidly converging series of elementary terms. Numerical examples and case studies are presented that validate the algorithm, illustrate its rapid convergence, and bring to light the effect of changing several physical and geometrical parameters on the reflection, transmission, and absorption characteristics of the structure.