A cavity resonator with input and output couplings represents a two‐terminal‐pair network with an infinite number of natural modes of oscillation. In some cavities of special shape, a number of degenerate modes with identical natural frequencies can be found. In a single cavity, various numbers of these degenerate modes can be coupled together to form a chain of coupled circuits by perturbing the otherwise ideal geometrical configuration of the cavity. The filter behavior is prescribed, and the two‐terminal‐pair network realizing this is obtained by a process of synthesis.