Relativistic core-potential calculations have been carried out on Omega states resulting from the interaction of Xe* (5p(5)6s, P-3, P-1) with ground-state Kr atoms as well as for the system Ar* (3p(5)4s, P-3, P-1) with ground-state Ne, using different basis sets and configuration interaction procedures. The present calculations on ArNe, employing larger sets of Rydberg functions than those of the previous calculations, yield totally repulsive potentials for the excited states of ArNe. Similar calculations on XeKr obtain shallow minima (600-860 cm(-1)) in the potential energy curves of the excited states at large internuclear distances (6.9-7.8 bohr). Dipole transition moments have been calculated and strong radiative transitions are predicted from excited states to the ground state. The 1(I) state, correlating with the metastable P-3(2) state of Xe is found to have a small but nonzero dipole transition moment at short and intermediate nuclear distances leading to a radiative lifetime for the v=0 level of this state of 21.0 mus.