Abstract. Under conditions of Anomalous X-ray Transmission (known as the Borrmann Effect), an X-ray standing wave is set up inside a crystal, leading to a strong reduction in electric dipole absorption. We show that electric quadrupole absorption is not similarly diminished and is thus relatively enhanced by a large factor. Absorption measurements, made under thick-crystal Laue (transmission) diffraction conditions in Gd₃Ga₅O₁₂ (GGG) and Y₃Fe₅O₁₂ (YIG), show a range of spectral features that can be assigned unambiguously to electric quadrupole events. This phenomenon, which seems to have been overlooked for decades, opens up new possibilities for studying important electronic states with hard x-ray beams. In this paper, we outline the origin of the effect and a phenomenological description of its temperature dependence, and consider the possibility of measuring the angle dependence of enhanced quadrupole absorption.