Abstract
A strong anomaly is predicted in absorption (scattering) of electromagnetic waves (photons) or acoustic waves (phonons) by quantum-mechanical particles in tunneling states, when an additional classical wave is applied with certain discrete values of the ratio of the wave amplitude to its frequency and the earlier revealed "coherent tunneling destruction" occurs. The anomaly is that the absorption (scattering) vanishes in the presence of the classical wave in such systems, e.g., in glasses.