The 73/27 random copolyester based on 4-hydroxybenzoic acid (HBA) and 6-hydroxy-2-naphthoic acid (HNA) shows a fast, dispersed relaxation process on the picosecond time scale. The underlying motion is difficult to determine unambiguously, but the data are consistent with translation of chain segments in a direction that is perpendicular to the chain direction. As the temperature is increased from the beta transition (303 K) to the glass transition, T-g (381 K), the dispersion stays constant and the average relaxation time increases slightly. At T-g the dispersion increases abruptly to a new constant value, and the average relaxation time increases noticeably with temperature up to the nematic melt transition, T-m (553 K). This unusual behavior is probably connected to the appearance of a slow relaxation process that becomes discernible above T-g. The characteristic length of this slow process remains constant between T-g and T-m at a value that corresponds to the interchain spacing close to T-m. This observation is consistent with a crankshaft motion of neighboring aromatic groups. As the amplitude of this motion increases, the average barrier to translation perpendicular to the chain direction becomes higher, causing longer relaxation times for the fast process. The slow crankshaft rotation thus appears to cause the dispersion of the fast translational process.