The frequency dependence of the first molecular hyperpolarizability beta of a thiophene based charge-transfer chromophore has been measured by using a number of excitation wavelengths emitted from an optical parametric amplifier pumped by a 1 KHz 130 fs Ti/sapphire laser. The excitation wavelength covers the resonance and nonresonance region of the charge transfer chromophore. beta shows a maximum on the red side of the charge transfer electronic absorption band. A comparison of the experimental result with a recent proposed calculation involving the Kramers-Kronig transformation of the charge-transfer absorption spectrum is made. It is found that while the Kramers-Kronig transformation analysis predicts a correct position of the beta maximum, it does not yield an agreement in the resonance region of the frequency dependent first molecular hyperpolarizability. (C) 2003 American Institute of Physics.