Absorbable polyester fibers, braids, and surgical meshes with prolonged strength retention have been developed. These devices are preferably derived from biocompatible copolymers or homopolymers of 4-hydroxybutyrate. These devices provide a wider range of in vivo strength retention properties than are currently available, and could offer additional benefits such as anti-adhesion properties, reduced risks of infection or other post-operative problems resulting from absorption and eventual elimination of the device, and competitive cost. The devices may also be particularly suitable for use in pediatric populations where their absorption should not hinder growth, and provide in all patient populations wound healing with long-term mechanical stability. The devices may additionally be combined with autologous, allogenic and/or xenogenic tissues to provide implants with improved mechanical, biological and handling properties.