The wavelength dependence of the cubic nonlinearity of ligated platinum-terminated polyynes trans, trans-{(P-MeC6H4)(3)P}(2)(p-MeC6H4)Pt(C C)(n)Pt(p-C6H4Me){P(p-C6H4Me)(3)}(2) (n = 3-6, 8, 10, 12) has been examined by femtosecond Z-scan studies in the wavelength range 520-1500 nm and the results rationalized by density functional theory calculations on the model complexes trans, trans-(H3P)(2)(C6H5)Pt(C C)(n)Pt(C6H5)(PH3)(2) (n = 2-8, 10, 12). Although the final states for one- and two-photon transitions are not the same in these centrosymmetric molecules, the Z-scan studies reveal coincidences in one-photon absorption with features in the frequency dependencies of both real and imaginary parts of the cubic hyperpolarizability, as well as inflections in the frequency dependencies of the real part of gamma that correspond to resonances in the imaginary part of gamma. The theoretical studies suggest that the linear absorption spectra are dominated by (XAg)-Ag-1 -> n(1)B(3u) transitions, with the first state of B-3u symmetry playing a steadily diminishing role upon oligoyne chain lengthening. The theoretical studies also predict a red-shift of two-photon absorption (TPA) profile with increasing conjugation length, and a significant enhancement on proceeding from the shortest to the longest chromophore, trends that are observed experimentally. The experimental low-energy TPA maxima for these complexes can be approximated by a simple Gaussian profile. The sp-carbon chain-length dependence of linear and nonlinear absorption maxima enable an estimate (neglecting saturation) of 660 and 1000 nm for the infinite carbon chain, carbyne.