Pprimary safety outcome of the study: frequency of hemorrhage. Design and methods: Following a first AV graft thrombosis and successful thrombolysis with angioplasty, patients on chronic hemodialysis will be randomized to s.c Enoxaparin (Clexane) 0.5 mg/1kg of body weight per day or control group (not on Clexane). Patients will be followed for a year or till next AV graft thrombotic occlusion, if it occurs before. In both groups we will compare time periods in months between first and recurrent thrombotic events of AVG by evaluation the difference between two sample means. Also interim analysis of AV grafts patency between the two groups will be evaluated at different time points: three, six and twelve months after randomization. Patients in both groups will receive unfractionated heparin during dialysis session to prevent thrombosis of extracorporeal circulation. Patients from Enoxaparin group will receive a half dose (500 units/hour) to prevent possible risk of bleeding during the session. Before randomization all patients will be evaluated for hypercoagulability state which will include: Factor V Laden deficiency, Anti phospholipid antibodies (APLA), Antithrombin III deficiency and Protein C/S deficiency.