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The coupling effects in bilayer thick metal (silver) films perforated with rectangular nanohole arrays are investigated using the finite-difference time-domain technique. Many interesting light phenomena are observed as the distance between the metal rectangular nanohole arrays varies. Coupling effects are found to play very important roles on the optical and electronic properties of bilayer metal rectangular nanohole arrays: antisymmetric coupling between surface plasmon polaritons near the top and bottom film plane, and antisymmetric coupling between localized surface plasmon resonances near the two long sides of the rectangular hole, are probably excited in each layer of bilayer metal rectangular nanohole arrays; antisymmetric and symmetric magnetic coupling probably occur between the metal rectangular nanohole arrays.