The transmission spectra of rhombohedral 0.71 Pb(Mg1/3Nb2/3)O-3-0.29PbTiO(3) (PMN-0.29PT) and tetragonal PMN-0.38PT single crystals were obtained in the main crystallographic directions (0 0 1), (1 1 0) and (1 1 1). The absorption coefficients were computed and the optical bandgaps were calculated in both direct and indirect transitions. The energy of phonons contributing in the indirect transition was also calculated. For PMN-0.38PT single crystal in all the three directions, the values of direct bandgaps E-gd are all slightly lower than those of PMN-0.29PT single crystal, while the indirect bandgaps E-gi are all higher. For different crystallographic directions, the values of Egi for (1 1 0)-direction are lower compared with (0 0 1) and (1 1 1) directions, both for PMN-0.29PT and PMN-0.38PT single crystals. Some discussions about the B-site cation d-orbits and the O-anion 2p orbits that determine the basic energy level of the single crystals are presented. The optical transition mechanism was also discussed. (c) 2005 Elsevier B.V. All rights reserved.