Molecular dynamics simulations of a model main-chain liquid crystalline polymer (LCP) and of a low molecular weight analogue have been carried out using an efficient parallel algorithm. A main-chain LCP is formed with the help of Gay-Berne mesogenic units connected to each other through flexible methylene spacers. We have studied the effect of varying the spacer length, and have examined the region of the isotropic-liquid crystalline transition. Our preliminary results indicate that liquid crystalline ordering may occur spontaneously on lowering the temperature, and that odd-even dependences of thermodynamic properties on spacer length occur, in agreement with existing experiments. Local orientational time correlation functions, as well as local translational mobility, have been studied both for the mesogenic elements and the bonds in the flexible spacer. The anisotropy of both orientational and translational local dynamical properties have been compared viith theoretical predictions and with Brownian dynamics results for a freely jointed chain in a liquid crystalline orienting field.