lThe first off-resonance hyperpolarizabilities (beta (0)) of bisubstituted carotenoids are computed and analyzed using a quasiparticle, collective electronic oscillators (CEO) representation. The few oscillators which dominate the response are identified by solving the time dependent Hartree-Fock equations for the reduced single electron density matrix. The variations of these oscillators and the relevant anharmonicities with bridge length are studied. The present approach does not suffer from the difficulties which prevent the development of a simple intuitive picture in the:commonly used sum-over-states expressions (i.e,, strong interference effects and unphysical size scaling of various contributions). Displaying the CEO in real space provides an intuitive picture of the origin of the nonlinear response and the scaling and saturation of beta (0) for large sizes.