Variable-temperature C-13 NMR spin-lattice relaxation times, T-1, and nuclear Overhauser enhancements (NOE) at two magnetic fields have been recorded for the amorphous phase of semicrystalline poly(4-hydroxybutyrate), P4HB, and two random copolymers : poly(3-hydroxybutyrate-co-4-hydroxybutyrate) with 18% (P3/4HB-18) and 69% (P3/4HB-69) 4hb units. The T-1 and NOE data were successfully interpreted by the DLM model in terms of conformational transitions and librational motions of the backbone C-H vectors. The mobility of both the 3hb and 4hb units was found to increase with increasing 4hb content of the copolymer. In both copolymers, the segmental motion of the 4hb unit was found to be 2-4 times faster than that of the 3hb unit, thus reflecting the local character of the segmental motions that affect C-13 relaxation in bulk polymers. In addition, the segmental dynamics followed the Williams-Landel-Ferry equation, indicating that they are involved in the glass transition phenomena. Literature P3HB dynamic modeling data adhere to the Williams-Landel-Ferry data presented here, indicating that P3HB in bacterial inclusions has a T-g similar to that of the extracted material.