One of the greatest problems in renal transplantation is the shortage of donor kidneys. Kidneys of non-heart-beating donors (NHB) are a possible solution, but transplantation is accompanied with a high percentage of acute renal failure, caused by ischemia-reperfusion injury. The increased ischemia-reperfusion injury results in an increased immune activation, which can lead to more injury of the kidney and additional acute rejections. The hypothesis of this trial is that ischemia-reperfusion injury can be diminished by ATG. ATG could have additional favourable effects. To investigate this half of the patients is treated with additional ATG to the standard immunosuppressive treatment. Calcineurin inhibitors are not diminished during the first days after transplantation to investigate whether ATG has special effects on ischemia-reperfusion injury.