Extended bis(donor)-substituted squaraine chromophores exhibit very high two-photon cross-sections (as high as 33 000 GM) in the near-IR; these can be attributed to the combination of large transition dipoles with small detuning energies. The modulus of the third-order nonlinear optical susceptibility at 1.3 mum has been found to be 7.0 x 10-11 esu for one of these chromophores.