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The response of a pair of directly interacting ring resonators, side-coupled to a waveguide, is investigated analytically for the first time. Owing to the direct interresonator coupling, counterpropagating waves are excited in each resonator, resulting in a complex filter behavior that can be totally reflective or transmissive at certain resonant frequencies. Using the scattering matrix formalism, we show that a variety of single- to four-peak reflection profiles can be obtained by appropriate tuning of the involved coupling coefficients. The predictions are validated by means of a full-wave integral equation analysis.