Successive magnetic phase transitions were found in the Kagome lattice antiferromagnets RFe(3)(OH)(6)(SO4)(2) [R = NH4, Na, K]. The temperature dependence of the susceptibility has two cusps around 60 K for each compound. The X-ray diffraction patterns and the quadrupole resonance spectra show that the transitions are not caused by a structural change. The presence of these transitions was confirmed by NMR experiments. The NMR spectra show the development of magnetic ordering below the upper transition temperature. Ln the low-temperature phase the nuclear magnetization does not relax exponentially, which may suggest a domain structure of 120 degrees spin structure due to degeneracy on the Kagome lattice. The successive transitions may be caused by a small Ising-like anisotropy in the Heisenberg antiferromagnet.