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The interaction between plane waves and multilayer elliptic cylinders with one or more layers made of metamaterials is considered. An analytical solution is proposed, which extends to double-negative metamaterials an efficient recursive procedure previously developed for double-positive dielectrics. Two cases are considered: multilayer dielectric cylinders and perfectly conducting cylinders with a lossy dielectric coating. Numerical results and comparisons are provided concerning both the internal field and the scattering cross section per unit length, allowing a significant assessment of the scattering properties of metamaterials.