Benzylic amide catenanes are a class of synthetically-accessible interlocked molecular rings which can rotate one through the other depending on the nature of the local environment. The rings contain four phenyl units each and interlocking also affords their packing in novel, highly interacting ways that may lead to unexpected properties thus opening up the possibility of developing new materials. Third harmonic generation in benzylic amide catenane solutions was measured at a wavelength of lambda = 1064 nm, with the fundamental and the harmonic wavelengths in the region of transparency of the material. The thoroughly non resonant value of the hyperpolarisability gamma(-3 omega; omega, omega, omega) was found to be (6.5 +/- 0.7) x 10(-35) esu with a neg ligible imaginary part, in agreement with the value of (6.8 +/- 0.9)x 10(-35) esu calculated from a bond-additivity model of hyperpolarisability. The static second order hyperpolarisability predicted by a Molecular Orbital model was about a factor four less than the experimental value. Second hyperpolarizability values of several solvents were also measured at the fundamental wavelength of lambda = 1061 nm.