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We demonstrate a new class of low-profile frequency selective surfaces (FSS) with an overall thickness of lambda/24 and a third-order bandpass frequency response. The proposed FSS is a three layer structure composed of three metal layers, separated by two electrically thin dielectric substrates. Each layer is a two-dimensional periodic structure with sub-wavelength unit cell dimensions and periodicity. The unit cell of the proposed FSS is composed of a combination of resonant and non-resonant elements. It is shown that this arrangement acts as a spatial bandpass filter with a third-order bandpass response. However, unlike traditional third-order bandpass FSSs, which are usually obtained by cascading three identical first-order bandpass FSSs a quarter wavelength apart from one another and have thicknesses in the order of lambda/2 , the proposed structure has an extremely low profile and an overall thickness of about lambda/24 , making it an attractive choice for conformal FSS applications. As a result of the miniaturized unit cells and the extremely small overall thickness of the structure, the proposed FSS has a reduced sensitivity to the angle of incidence of the EM wave compared to traditional third-order frequency selective surfaces. The principles of operation along with guidelines for the design of the proposed FSS are presented in this paper. A prototype of the proposed third-order bandpass FSS is also fabricated and tested using a free space measurement system at C band.