During the past ten years progress in the field of vascular surgery and immunology has been such, that a steady improvement in the results of clinical organ transplantation can be observed. Also when a life threatening disease of the liver is present, liver transplantation may be considered. In general these diseases may be described as follows: Necrosis of the liver, acute or sub-acute, can give rise to a progressive loss of the liver function. The causal factors are very often unknown. Sometimes certain hepatotoxins can be indicated as the cause. Halothane, for instance, may give rise to acute hepatic necrosis of the liver (Silverman 1975). Viral hepatitis can also produce such serious damage to the liver, that it endangers life.