We have produced recently the very first experimental evidence that X-ray Natural Circular Dichroism (XNCD) can be detected in both uniaxial and biaxial gyrotropic single crystals. XNCD signals are to be assigned to electric dipole-electric quadrupole E1.E2 interference terms which can be quite significant in the X-ray range whereas there can hardly be any detectable contribution of the electric dipole-magnetic dipole E1.M1 terms which dominate CD at optical wavelengths. For heavily absorbing single crystals, the differential absorption between left-handed and right-handed circularly polarized X- ray photons cannot be measured in transmission but circular dichroism can still be detected in fluorescence excitation spectra. XNCD and Fluorescence detected X-ray Natural Circular Dichroism (Fd-XNCD) spectra are strictly identical for uniaxial crystals such a lithium iodate ((alpha) -LiIO3) but this is only true to the first order for biaxial crystals such as potassium titanyl phosphate (KTP). Such difficult experiments became feasible only with the development of powerful helical undulator sources and with a careful optimization of all components of the beamline.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.