A surface access double hemostatic valve comprises a first hemostatic valve mounted in the wall of a hemodialysis graft, a chamber extending from the first hemostatic valve, and a second hemostatic valve mounted at the distal end of the chamber for positioning at the surface of the skin of the patient. The graft having the surface access double hemostatic valve mounted thereon is surgically installed in the skin of the patient. Thereafter the interior of the chamber is sterilized and a blood access member is inserted through the second hemostatic valve, through the chamber, through the second hemostatic valve, and into the interior of the graft for access to blood flowing therethrough to effect hemodialysis.