Second Harmonic Generation of light (SHG) is used as a probe to study the structure of the nematic, cholesteric or smectic mesophases of various liquid crystals, with non centro-symmetric molecules. In one case (cholesteryl 2-(2-ethoxy ethoxy) ethyl carbonate) where SHG has already been reported, it is shown that SHG occurs in the crystalline rather than the mesomorphic phase. In all cases, no evidence is found of any SHG in any mesophase. Consequently, these are probably centrosymmetric by compensation, as is the normal liquid phase.