The frequency dependent hyperpolarizability of typical donor-acceptor organic nonlinear optical molecules is commonly represented by a nonresonant two-level model, first presented by Oudar and Chemla. We discuss how this model can be extended into the resonant regime, including cases where the molecular transition is described by an inhomogeneously broadened peak. A resonant measurement of hyperpolarizability by electric field induced second harmonic generation (EFISH) is demonstrated, as well as the more conventional off-resonance EFISH. The theoretical model correctly predicts both the amplitude and phase of the resonant hyperpolarizability measured by EFISH. We also show that both on-resonance and off-resonance EFISH yield the same hyperpolarizability extrapolated to the zero frequency limit. (C) 2000 American Institute of Physics. [S0021-9606(00)01009-6].