Nonlinear optical properties of nematic liquid crystals (NLC) have been investigated. A technique for efficient laser frequency conversion in a microscopic NLC volume deposited on an optical fibre end face is experimentally demonstrated. An efficient design of a compact NLC-based IR frequency converter with a fibre input and achromatic collimator is proposed and implemented. Simultaneous generation of the second and third harmonics is obtained for the first time under pumping NLC by a 1.56-mm femtosecond fibre laser. The second-harmonic generation efficiency is measured to be about 1 %, while the efficiency of third-harmonic generation is several tenths of percent. A strong polarisation dependence of the third-harmonic generation efficiency is revealed. When pumping NLC by a cw laser, generation of spectral supercontinua (covering the visible and near-IR spectral ranges) is observed. The nonlinear effects revealed can be due to the light-induced change in the orientational order in liquid crystals, which breaks the initial symmetry and leads to formation of disclination structures. The NLC optical nonlinearity is believed to be of mixed orientationalelectronic nature as a whole.