The absorption spectra were measured in beta '-Tb-2(MoO4)(3) in the non-polarized light in the magnetic field H <= 20 T along the [0 0 1] and [1 1 0] axes at T = 4.2 and 1.7 K. The wave vector of the light was parallel to the magnetic field. The experimental field dependences of the wave numbers of the absorption peaks v(i)(H) were obtained. The analysis of those dependences shows that the excited multiplet D-5(4) of Tb3+-ion in the crystal field of beta '-Tb-2(MoO4)(3) can be considered as consisting from five singlets and two quasi-doublets. The field dependences of the energy levels E-i(H) of the D-5(4) multiplet were obtained from the experimental data in the magnetic field along the [0 0 1] axis. The experimental dependences E-i(H) can be described well by the theory of the magnetism of singlets. (C) 2005 Elsevier B.V. All rights reserved.