Electronic structures of the weakly bound Rn, were calculated by the two-component Moller-Plesset second-order perturbation and coupled-cluster methods with relativistic effective core potentials including spin-orbit operators. The calculated spin-orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin-orbit effects On D-e (0.7-3.0 meV) and R-e (-0.4 similar to -2.2 Angstrom) of Rn-2 are comparable to previously resorted values based on configuration interaction calculations. A two-component approach seems to be a promising tool to investigate spin-orbit effects for the weak-bonded systems containing heavy elements. (C) 1999 John Wiley & Sons, Int. Int J Quant Chem 72: 139-143, 1999.