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The results of both numerical and analytical examination of Wood-type anomalies for diffraction at crossed gratings are presented. The general reflective properties of the double periodic structures formed by modulation of the electromagnetic properties of the surface are investigated. The dependence of the reflection coefficients on the grating orientations, periods, form and modulation magnitudes, and on the angle of incidence is examined. In particular, it is shown that the total suppression of the specular reflection (TSSR) of an arbitrary polarized incident wave is possible for normal incidence and corresponding specific values of the gratings parameters are found.