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Summary form only given.The study of the nonlinear interactions in periodic structures has gained considerable interest in the past few years. This is due to the finding of the novel kind of nonlinear solitary waves that are propagated at Bragg frequency within the linear forbidden gap band of the periodic medium. It has been shown that gap solitons and oscillating solitary waves exist in one-dimensional structures with resonant and Kerr nonlinearity. These waves are formed by two counterpropagating coupled Bragg modes. Here we investigate theoretically the dynamics of formation and propagation of nonlinear solitary waves in the general case of two-wave diffraction problem in two- and three-dimensional periodic resonant structures.