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This paper introduces several different design methodologies for multiband artificial magnetic conducting (AMC) surfaces. The paper begins by investigating the multiband properties exhibited by a conventional electromagnetic bandgap (EBG) AMC that consists of a frequency selective surface (FSS) on top of a thin dielectric substrate with a PEC back plane. The higher-order resonances associated with these surfaces have not been discussed in detail to date, as previous research has been concerned only with exploiting the primary resonant frequency. However, it will be shown that by understanding and making appropriate use of these higher order resonances, it is possible to design multiband AMC surfaces that work for nearly any desired combination of operating frequencies. The first multiband AMC design approach that will be considered is based on the introduction of FSS screens that have fractal or nearly fractal unit cell geometries. This is followed by a more general and robust genetic algorithm (GA) technique for the synthesis of optimal multiband AMC surfaces. In this case, a GA is used to evolve multiband AMC surface designs by simultaneously optimizing the geometry and size of the FSS unit cell as well as the thickness and dielectric constant of the substrate material. Finally, several examples of multiband AMC surfaces are presented, including some practical dual-band and tri-band designs genetically evolved for operation at GPS and cellular frequencies, as well as an example illustrating the success in creating a multiband AMC surface with angular stability.