Ab initio calculations of RgF(n) (Rg = Xe, Rn, and Element 118; n = 2, 4) were performed using relativistic effective core potentials and two-component HF, MP2, CCSD, and CCSD(T) methods. Geometries were optimized at the HF level with and without effective spin-orbit operators. The D-4h, structures of all tetrafluorides and the linear difluorides are local minima with and without spin-orbit interactions. Spin-orbit contributions makes the T-d form of (118)F-4 another local minimum with the energy comparable to that of the D-4h one. The spin-orbit interactions stabilize the (118) fluorides by a significant margin (similar to 2.0 eV) and the Rn fluorides by 40-60% (0.2 similar to 0.4 eV) of the stabilization energy obtained at the corresponding scalar relativistic level. For (118)F-4, the vibrational frequency of the B-2u mode of the D-4h form decreases from 143 to 20 cm(-1) upon inclusion of the spin-orbit interactions, and a doubly degenerate mode of the T-d structure, which is stable only with the inclusion of spin-orbit interactions, has the frequency of 34 cm(-1), indicating that the (118)F-4 molecule is very flexible due to spin-orbit effects.