The electron paramagnetic resonance (EPR) parameters (g factors g(parallel to), g(perpendicular to) and hyperfine structure constants (171)A(parallel to), (171)A(perpendicular to), (173)A(parallel to) and (173)A(perpendicular to)) for three Yb(3+) centers, one cubic (center I) and two trigonal (centers II and III). in ThO(2) and CeO(2) crystals are studied from a complete diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are added to the classical Hamiltonian and the crystal-field parameters are calculated from the empirical superposition model. From the studies, the EPR parameters for these Yb(3+) centers in ThO(2) and CeO(2) crystals are reasonably explained, the defect model for the trigonal Yb(3+) center II suggested in the previous paper is confirmed and the defect structure of center II are also obtained. The theoretical hyperfine structure constants A of two Yb isotopes for centers II and III are suggested and remain to be checked by further experiments. The results are discussed. (C) 2010 Elsevier B.V. All rights reserved.