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Diffraction of obliquely incident waves by a perfectly conducting strip of infinite length immersed in either 1) an unbounded bianisotropic medium or 2) a bianisotropic cylinder is investigated. Systems of singular integral-integrodifferential equations having the induced surface current densities as the unknowns are derived by following several independent formulation techniques. Discretization is carried out using moment-method-oriented techniques applied to singular integral equations. The matrix elements are given either in closed form or by exponentially convergent series which require no numerical integration. Moreover, the algorithms are found to converge exponentially versus matrix size. Numerical results are presented which show the effect of changing either the degree of bianisotropy or the strip width and orientation on the scattering characteristics.