The local motions of terpolyesters based on varying amounts of hydroquinone, hydroxybenzoic acid and isophthalic acid units were investigated using high-resolution solid-state C-13 NMR. At temperatures below the glass transition temperature, the mesomorphic polymer having equal amounts of the three units demonstrates partial motional averaging of the chemical shift tensors of the aromatic carbons which indicates the existence of oscillations for both para- and meta-substituted rings. The oscillations of the para-substituted phenyl rings appear to be correlated with the motions of the adjacent carbonyl groups. At high temperature there also occurs small-amplitude main-chain reorientations which are likely to be involved in the glass-transition phenomenon. These motions were also observed in the amorphous phase of other compositions of the terpolyester leading to conventional semicrystalline polymers.