Circular dichroism anisotropy was studied both theoretically and experimentally for the complexes of DNA and dsRNA with dyes (proflavine, 2,7-di-t-butyl proflavine, "Hoechst-33258") and antibiotics (distamycin A, netropsin and olivomycin). Theoretical analysis showed that general features of CD anisotropy, revealed in the previous studies (CD components--delta epsilon parallel to and delta epsilon perpendicular--are ten times or more bigger than the CD-effect without orientation, and delta epsilon parallel to approximately 2 delta epsilon perpendicular) are due to the existence of a specific effect named "latent" optical activity (LOA). This effect can be observed in many cases of non-chiral symmetrical chromophores if they are oriented. The effect is due to the excitation of an electrical dipole transition and a perpendicular magnetic dipole transition (or quadrupole transition) of a molecule. The amplitude and the sign of the LOA-effect depends on the orientation of the chromophores with respect to the light beam; with a random orientation the mutual compensation of LOA-effects of different chromophores happens and no LOA-effect appears. The analitycal expressions relating the value of LOA-effect of the system with electronical characteristics of the chromophores and the geometrical parametra of their arrangement was obtained. The experimental data obtained for the oriented complexes of DNA and dsRNA with proflavine made it possible to determine an angle between the chromophore and the plane perpendicular to the DNA axis--gamma. For the calf thymus DNA gamma = = + 1.8 +/- 0.4 degrees, for the phage T2 DNA gamma = + 2.2 +/- 0.4 degrees, and for phage f2 dsRNA gamma=--3.5 +/- +/- 0.5 degrees. These results, obtained at relatively low concentrations of the bound proflavine (r approximately 0.01), are in accordance with the intercalating mode of the dye binding. A study of CD anisotropy of DNA complexes with other ligands showed that many different chromophores possess LOA-effect. This phenomenon can be used to obtain both spectroscopic and structural information about the systems similar to those reported here.