By measuring the third-order nonlinear optical susceptibility χ1111(3)(-ω,ω,ω,-ω) at 1.06 μm of various solutions of C60 and C70 in benzene, we place limits on the hyperpolarizabilities of these molecules of -180≤(γ111160C/γ1111benzene)≤60 and -120≤(γ111170C/γ1111benzene)≤250, respectively. These limits assume that 1.06 μm is near the long-wavelength limit where χ(3) must be real. We also give limits on the imaginary parts of the hyperpolarizabilities, making no assumptions about their phases. The magnitudes of these limits are two orders of magnitude smaller than several values that have been published. We checked our experimental technique by measuring the nonlinear susceptibility of CS2-benzene mixtures and found the value for χCS2(3)/χbenzene(3) of 5.7±0.5. This agrees with parameters deduced from many different experiments published previously.