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Recently an impedance and admittance integral equation formulation for planar steps has been published. It leads directly to a reduced multi-mode matrix representation of cascaded uniform waveguides involving only a small number of accessible, or interacting, modes. In this paper we will generalize the integral equation approach to cavities. This enables to use the same concept also in waveguide networks including bifurcations like T-Junctions, Magic-Ts, etc.