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The scattering of a plane electromagnetic wave by an infinite elliptic dielectric cylinder is examined using two alternative methods. In the first the electromagnetic field is expressed in terms of elliptical-cylindrical wave functions while in the second, a shape perturbation method is applied by expressing the field in terms of circular-cylindrical wave functions only and the equation of the elliptical boundary in polar coordinates. Analytical expressions are obtained for the scattered electromagnetic field and the various scattering cross-sections, when the solution is specialized to small values of the eccentricity h = c/2a (h ?? 1), with c the interfocal distance of the elliptic cylinder and 2a the length of its major axis. In this case the scattered field and the scattering cross-sections expressions have the form of S(h) = S(0)[1+g(2)h2 + g(4)h4 + O(h6)], where the expansion coefficients g(2) and g(4) are given by exact, closed form expressions. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters.