The relative biological effectiveness (RBE) has been considered for three kinds of cell radiation damages: subdamages (sublethals), one-track, and two-track lethal damages. In contrast to the "dual theory", which postulates the square relation between the lethal damage yield and the specific energy, it is assumed that the one-track lethal yield is linearly related to the specific energy per cell nucleus. As a result, the identical dependence has been obtained of both one-track lethals and subdamages on specific energy and absorbed dose. It is established that RBE for all three kinds of damages does not depend on the radiation dose. It is shown that RBE for subdamages and one-track lethals depends on LET of radiation only, and involves molecular parameters of sensitive cell structures. Within the limits of this assumption, the relations are general for all the types of eukaryotic cells. These can be used for a further development of the RBE theory, with spectra of LET, the track structure of charged particles, the contribution of delta-electrons etc being taken into consideration.