The influence of absorption upon behavior of the reflection coefficient in water for an anisotropic periodically multilayered medium is studied. From observing a trough of the experimental reflection coefficient of a carbon/epoxy composite immersed in water, the propagation modes of the Floquet waves in an infinite anisotropic periodically multilayered medium in vacuum have been studied. This was explained by a mode that we called themultilayeredRayleighmode. This mode results from a combination of the Floquet waves which propagate in a periodically multilayered medium. This occurs when all the Floquet waves are inhomogeneous. Analyzing the results obtained in the isotropic case permits the more complicated cases to be explained. By analogy with the isotropic case, themultilayeredRayleighwaveis related to the poles and the zeros of the reflection coefficient. The existence of a critical attenuation becomes evident when the reflection coefficient in water for the multilayered medium reaches zero. ©1995 American Institute of Physics.