The non-linear optical properties of several cholesteric and nematic liquid crystals are studied in laser experiments on generation of secondand third-harmonic radiation. No secondharmonic is observed in any of the liquid crystal mesomorphic phases, indicating that the local molecular ordering in these phases is centrosymmetric. The generality of this result to datediminishes the potential of liquid crystals as nonlinear materials. Large intensity changes ofthird harmonic are observed at several phase transitions, and their possible origins are discussed. Tentative results are presented on experiments to utilize the high optical rotatory power of the cholesteric phase to obtain phase matching in third-harmonic generation.