Dynamic mechanical and dielectric analyses in polyester liquid crystalline polymer(LCP) and short glass fibre reinforced polyester liquid crystal composites have been performed in the temperature range form -100 to 250℃. There are the multiple transitions in samples, which are denoted as αm, βm for dynamic mechanical analysis and αe, βe, βe' for dielectric analysis in conformity with reducing temperature. For dynamic mechanical analysis, αm transitions is the glass transitions of samples, βm relaxation is likely to be related to the flexibility of main chain motion. The both LCP and LCP composites exhibit strong dynamic mechanical anisotropy due to molding flow direction. As the glass fibre contents increase, the reinforcing effect is improved, however the law of mixture is shown to be not valid. Dielectric analysis, αe, βe relaxations are likely to be related to the flexibility of dipole motion of main chain, and βe' relaxation is expected to be not the ordinary relaxation of glass state but phase transition.