A simple model based on Huckel theory that quantitatively accounts for linear polyene 2(1)A(g) and 1(1)B(u) excitation energies has been used to predict nonlinear optical response of this class of molecules. The essential elements of the model are the use of alternating resonance integrals to obtain the proper chain-length dependence of the 1(1)B(u) highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) excitation energy and mixing of the HOMO to LUMO + 1, HOMO-1 to LUMO and HOMO to LUMO double-excitation configurations to describe the 2(1)A(g) state. Even though one of the appealing features of this model is the ease with which it can be extended to include vibrational levels, this contribution focuses on calculations carried out in a purely electronic basis. Despite the extreme simplicity of the model, it reproduces many of the results of much more elaborate computations including the fact that a higher lying (1)A(g) state has substantially larger 2-photon absorptivity than does the 2(1)A(g) state and the fact that two photon resonance with the 2(1)A(g) state can provide significant enhancement of the nonlinear optical response of these molecules at wavelengths well below the one-photon absorption edge.