The Z-scan technique is used to extract the real and imaginary third order nonlinear susceptibilities, Re(chi )(3) and Im(chi )(3), respectively. A series of Z scans were conducted at 590 nm (near one-photon resonance) on a cumulene-containing polymer, poly(p- phenylene-1,4-diphenyl-1,2,3-butatriene) or PPC3, prepared in solution. At very high peak focal point intensities two- photon absorption is seen superimposed on a one-photon saturation signature in open aperture Z scans. A negative real third-order nonlinear susceptibility is also observed in closed aperture Z scans. We describe a procedure to extract the desired third-order nonlinear susceptibilities by conducting Z scans at various peak focal point intensities and then fitting the results by adjusting Re(chi )(3) and saturation intensity. Molecular second hyperpolarizability, is calculated to be (-1.4 + 2.2i) X 10-29 esu which is almost 40 times larger than that measured in a monomer equivalent, and scaling nonlinearly with chain length. Z scans were also conducted at 780 nm, (below one-photon resonance) on PPC3 and also gives a molecular second hyperpolarizability that is greater than that seen in the monomer. The higher value of molecular second hyperpolarizability measured near one-photon resonance is attributed to the existence of a real state at the first transition in a two-photon process.