Phase and relaxation transitions in ternary thermotropic LC copolyester were studied in a wide temperature range by means of dynamic mechanical relaxation, DSC, and X-ray analysis. Highly oriented fibers based on copolyester containing 45 mol% terephthalic acid, 45 mol% phenylhydroquinone, and 10 mol% n-hydroxybenzoic acid were used. The properties of both as-spun fibers and fibers annealed at high temperatures for a long time were characterized. The appearance of the mobility of the most rigid structural unit in the copolyester studied was shown to result in cooperative motion of chain fragments and to control glass transition temperature, which was equal to 180-degrees-C. Above this temperature, the transition from the initial mesomorphic structure (LC smectic B type) in the as-spun copolyester fibers into the nematic LC phase was observed, and copolyester gained the ability to flow. Crystallization in the copolyester samples induced by annealing at temperatures above 250-degrees-C involved the formation of two crystalline phases with rhombic structure, which were characterized by different parameters of unit cell. The maximal crystallinity of the samples did not exceed 35 - 40%. Melting of the crystalline phases was observed at temperatures above 300-degrees-C, and this process was shown to be accompanied by the formation of oriented nematic melt, which became isotropic above 400-degrees-C.