Highly-conjugated main chain polymers have been studied extensively in recent years as third order non-linear optical materials. However, in a non-centrosymmetric system such as a polyene which has been substituted with an electron donor and acceptor group, the relaxation of certain selection rules results in an increase in the static third order hyperpolarisibility. Consequently, there has been recent interest in the third order non-linear optical properties of materials more typically studied for their quardratic non-linear response. One of the driving forces for this work has been the possibility of producing single device substrates possessing significant second and third order non-linearities which could lead to highly integrated optical devices. We present the third order non-linear susceptibilities of some asymmetrically-substituted, side-chain liquid crystalline polymers, measured in amorphous thin films by third harmonic generation at 1064 nm and 1579 nm. The highest chi((3)) value of 1.02 x 10-(18) m(2)/V-2 from a polymer with an azo side group is expected to have some resonance contribution and is comparable with the non-resonant susceptibility of main chain polymers such as poly(phenylacetylene) and poly(p-phenylenebenzobislhiazole).