For a patient in the chronic programme of haemodialysis an uncomplicated accession to the vessels is the prerequisite for an optimum medical and social rehabilitation. Each form of a subcutaneous arteriovenous fistula is to be preferred to an epicutaneous shunt prosthesis. The percutaneous puncture of large vessels is necessary for the rapid connection to the dialyses in acute situations. In long-term treatments often all autologous accessions to the vessels are used up. Homologous substitution material for vessels is increasingly used also in patients ongoing dialysis. Apart from the methods for gaining homologous material is reported on first experiences in the application of homologous grafts of the umbilical vein and of a homologous vena saphena graft in patients undergoing dialysis.