AbstractPolydepsipeptides, alternating copolymers of an a-amino acid and a a-hydroxy acid, are an interesting group of degradable polymers. They have gained attention as potential degradable implant materials. Polydepsipeptides are expected to have better biocompatibility in vivo during the degradation process than aliphatic polyesters. Various depsipeptide-based polymers with or without pendant functional groups have been synthesized via ring-opening polymerization of corresponding morpholine-2,5-dione derivatives. The different polymer architectures of the polymers, for example, providing an alternating, random, diblock, triblock, or multiblock structure, can be obtained by appropriate selection of the polymerization reaction, which may be ring-opening or polyaddition. Recently, we synthesized thermoplastic phase-segregated copolymers with a multiblock structure containing polydepsipeptides and poly(e-caprolactone) or poly(p-dioxanone) segments via coupling of the respective diols using an aliphatic diisocyanate. The obtained multiblock copolymers showed good elastic properties at 25°C and 75°C. Furthermore, they exhibited a shape-memory capability. Here, we summarize the synthesis, biodegradation behavior and shape-memory properties of the multiblock copolymers. In addition, we introduce new combinations of depsipeptide/poly(ether)ester segments in multiblock copolymers. The depsipeptide-based multiblock copolymers have potential applications as biomaterials for controlled drug release, tissue engineering scaffolds, or base materials for biofunctional implants.