The laser induced fluorescence spectra of XeAr and XeNe have been measured near the Xe 6s[3/2](1) degrees - S-1(0) transition at 68 045.663 cm(-1). In XeAr, nine discrete peaks were observed, attributed to excitation to vibrational levels of the excited Omega=0(+) electronic state, merging into a continuum. From a Franck-Condon analysis, the potential for the excited Omega=0(+) state of XeAr was determined. It was found that this potential has a shallow minimum at long range [D-e’ = 28(1) cm(-1), r(e)’ = 5.44(7) Angstrom] with a shallow repulsive wall. The shallow repulsive wall is attributed to the influence of the XeAr+ ion core at short range. The role of the 6s Rydberg electron of Xe in determining the shape of the interatomic potentials of excited XeRg (Rg = a ran gas atom) is discussed on the basis of a simple model potential, in which the interatomic potential is described as the sum of a diatomic ion core (XeRg(+)) potential term and a term representing the exchange repulsion between the Rydberg electron and the rare gas moiety. For XeNe, only continuum spectra were observed, indicating that the upper states are not bound.