The possible use of glasses as the nonlinear optical material in all-optical switching calls for glasses with nonlinear refractive indices much higher than those of vitreous silica. Relatively high values of the nonlinear index coefficient, n2, have been found in Na2O-TiO2-Nb2O5-SiO2 glasses, in which n2 is completely dominated by the Ti-O and Nb-O bonds. We have investigated the nonlinear optical properties of R2O-TiO2-Nb2O5-SiO2 glasses as a function of the monovalent ion R (Na, K, Rb, Cs, TI). The results show that the dependence of n2 on R is larger than predicted from the empirical relation between n2 and n. An especially large enhancement of n2 is seen for T1. This can be explained by the difference in electronic configuration between TI (unfilled shell) and the alkali ions (filled shell).