C-13 NMR spectroscopy is used to study the local segmental dynamics in the bulk of biodegradable poly(4-hydroxybutyrate) and a random copolymer of 3-hydroxybutyrate and I-hydroxybutyrate that contained 18% 4-hydroxybutyrate units. The crystalline phase of the copolymer is shown by solid-state C-13 NMR to be comprised of 3HB units, in accord with reports based on X-ray diffraction. C-13 relaxation measurements indicate that the local dynamics in the amorphous phase are of different time scale for the two different types of monomer units in the copolymer. Furthermore, the segmental motions of the 4-hydroxybutyrate units are found to be slower in the copolymer than in the homopolymer.