Using two-color fluorescence dip spectroscopy, we observed two-photon absorption processes (TPA) in Rhodamine 6G occurring in concert with fluorescence depletion processes (FD). A nano-second pulse erase beam in the near-infrared region was applied to induce TPA together with FD. It was found that the fluorescence intensity strongly depends on the photon-flux of the erase beam and that the effective TPA cross-section for the nano-second laser pulse is smaller than that for a femto-second laser pulse. This phenomenon can be interpreted as resulting from FD induced by a multiple-excitation process.