Solutions of C-60 and C-70 exhibit a large third-order nonlinear response, even when investigated with low-power visible lasers. The remarkably large nonlinearity observed is attributed to a combined effect of thermally induced nonlinear refractive index changes and simultaneous nonlinear absorption. Fullerenes have the potential for applications in all-optical devices if they retain the same properties as in solution when dispersed in a transparent polymer matrix.