The synthesis and thermal properties of two new Liquid crystalline polyesters derived from bibenzoic acid and (R,S)- or (R)-3-methyl-1,6-hexanediol are reported. The phase behaviour was investigated by means of differential scanning calorimetry, X-ray diffraction and polarizing microscopy. The effect of the asymmetry introduced by the branched methyl group and that of the stereoisomerism on the type and stability of the mesophases formed are analysed. Both polymers exhibited smectic mesophases of different types depending on thermal history. The presence of an optically active pure diol along the chain gives rise to a more regular structure in comparison with the polymer synthesized from the racemic mixture.