Electro-optical Kerr effect data have been obtained for 6CB, 6CHBT, 6PCH, and 6BOBT at temperatures greater than the nematic-isotropic transition temperature. Using these data, the real parts of the third-order nonlinear susceptibility x((3)) are determined for all the liquid crystals. All the compounds had a positive Kerr constant, which increased with decreasing of temperature. The second-order phase-transition temperatures, T-*, were determined for these compounds. The replacement of aromatic ring by a flexible cyclohexyl group or a bulkier bicyclooctane has a marked effect on the birefringence. Hexyl 4-(4-isothiocyanato-phenyl) bicycle [2,2,2] octane, 6BOBT, with, the highest transition temperature, had the lowest Kerr constant. In contrast, hexyl cyanobiphenyl, 6CB, showed the largest Kerr constant (6BOBT -> 6CHBT approximate to 6PCH -> 6CB). The effect of the rigid core and polar head group of the liquid crystals was investigated.