Nonlinear transmission measurements of a solution of radical dimers of tetramethyl-tetrathiafulvalene, (TMTTF+)2, recorded with 9 ns laser pulses at 1064 nm are reported and interpreted on the basis of a multiphoton absorption process. One finds that the process can be interpreted with a sequence of three photon absorption, the first being a one photon absorption related to the intermolecular charge transfer process characteristic of the dimers and the second a two photon absorption from the excited state created with the first process. A model calculation allows one to obtain the value of the two photon absorption cross section which is found to be several orders of magnitude larger than those usually found for two photon absorbing systems excited from the ground state. These results show the importance of an excited-state population for obtaining large nonlinear optical responses.