The electron-spin-resonance (ESR) was measured for trivalentium neodymium dysporsium, erbium, and ytterbium in the single crystal samples of lithium niobiate. The measurements were made at X-band frequencies in the temperature range from 4K to 50K. Distinct hyperfine lines due to isotop Er-167, and weak hyperfine lines due to isotopes Dy-161, Dy-163, and Yb-171, Yb-173 were observed. The g factors and hyperfine parameters were obtained by use of the spin Hamiltonian and fitting to angular dependence of observed spectra. Moreover for LiNbO3 : Nd3+ g factors were verified for powder samples. According to these results some conclusions concerning sites in which rare earth ions are placed in the crystal lattice of LiNbO3 can be drawn.