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This paper presents a modular, direct, and accurate design technique for microwave dual-mode bandpass filters. The design is based on the generalized scattering matrix of each discontinuity in the structure. Different propagating modes in the same waveguide section are used in the representation of such matrices in order to facilitate the design. Different representations of the coupling matrix are also used. These are chosen to take into account the boundary conditions inside the cavity and the dominant physics of the problem at each stage. The loading of the resonances by the coupling elements is accurately calculated at each design step by exploiting a circuit based on propagation instead of resonance. Design examples of filters of fourth and eighth orders in rectangular and circular cavities are presented. Excellent initial designs are achieved with little or no need for any optimization.