In the past decade, the structural and electronic properties of monolayer-protected metal clusters, which can be produced size-selected in macroscopic amounts, have received a lot of attention. Their great potential for optical applications has been identified. In the high intensity regime, monolayer-protected metal clusters show pronounced nonlinear absorption and refraction. Naturally, these phenomena are wavelength-dependent, however, such dependence is largely unexplored. Here, we quantify the wavelength-dependent non-linear optical absorption and refraction cross sections of atomically precise Au25(DDT)18 and Au38(DDT)24 clusters, using the z-scan technique in combination with a tunable nanosecond laser source. Qualitatively different non-linear optical phenomena were found to take place at different excitation wavelengths (two-photon and excited-state absorption, intensity saturation and non-linear refraction). Both clusters have high nonlinear absorption cross sections at 532 nm, and present a (local) maximum at 640 nm, together with a maximum in the absorption saturation. The nonlinear refraction is always negative for Au25(DDT)18, while it changes sign for Au38(DDT)24. Depending on the wavelength, the underlying mechanism of the nonlinear absorption effects is two-photon absorption or excited state absorption. The obtained very high nonlinear cross sections, on the order of 107-109 GM, demonstrate the great potential of those clusters as nonlinear absorption or refraction materials in optical applications.