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In this paper, the hybrid finite element-boundary integral (FE-BI) method appropriate for modeling conformal antennas on doubly curved surfaces is developed. The FE-BI method is extended to model doubly curved, convex surfaces by means of a specially formulated asymptotic dyadic Green's function. The FE-BI method will then be used to examine the effect of curvature variation on the resonant input impedance of a cavity-backed, conformal slot antenna and a conformal patch antenna recessed in a perfectly conducting, electrically large prolate spheroid surface. The prolate spheroid shape provides a canonical representation of a doubly curved mounting surface. The numerical results for conformal slot and patch antennas on the prolate spheroid are compared as a function of curvature and orientation.