Based on the presented rigorous theory for two-dimensionally periodic (2DP) medium, characteristics of wave propagation in DWA were analyzed and studied in detail. Firstly, if there existed longitudinal wave vectr (k z≠0), the characteristics of interactions between space harmonics were analyzed, and dispersion relations between transversal wave vectors were obtained. Secondly, supposing transversal wave vectors were identical (k x=k y), the characteristics of interactions between space harmonics and stop-bands caused by them were studied comprehensively, and dispersion relations between longitudinal and transversal wave vectors were also analyzed and calculated when wave frequency varied. A very interesting conclusion of purely longitudinal propagation in DWA was obtained. The results have practical application values.