The invention relates to a stent-graft with a bioabsorbable structure and a permanent graft for luminal support and ‘treatment of arterial fistulas, occlusive disease, and aneurysms. The bioabsorbable structure is formed from braided filaments of materials such as PLA, PLLA, PDLA, and PGA and the graft is formed from materials such as PET, ePTFE, PCU or PU.