We measure two-photon absorption (2PA) spectra of wild-type green fluorescent protein, cyan fluorescent protein, and monomeric red fluorescent protein in absolute cross section values in a wide spectral range (lambda(2PA) = 550 - 1300 nm), and find, for the first time to our knowledge, a new S-0 -> S-n 2PA transition in all three proteins in the short-wavelength region. This transition is strongly resonantly enhanced, showing 2PA cross section values of similar to 20-160 GM, which are at least 2-4 times higher than those measured in the lowest energy (S-0 -> S-1) transition of corresponding proteins. We also show that the change of permanent dipole moment upon S-0 -> S-1 excitation (vertical bar Delta mu(10)vertical bar) can be deduced from 2PA cross section, providing a new tool for fast evaluation of vertical bar Delta mu(10)vertical bar in physiological conditions.