The difficulties associated with application of the risk concept are most pro nounced when the concept is used for the evaluation of so called Low Probabil ity/High Consequence Risks. These are the risks, found in the right bottom comer of the risk spectrum shown in Fig. 4. In this figure four risk spectra are shown, representing different types of risk bearing activities. In the area at the right bottom comer the event probability is so small and the consequences so high, or even unpredictable, that we touch upon the zero-times-infinity problem. Some people say, that it is just the benefit of the risk concept that we are able to quantify, and to justify, the risks associated with activities found in this area. Others, on the contrary, judge this area to be a forbidden one, because the event probability is smaller than can be verified within one generation’s period, and because the conse quences are expected to exceed the limits of "responsible stewardship". Aware of the fact that it is difficult to define what should exactly be meant by responsible stewardship, particularly because this is an issue intimately connected with people’s world view, it is considered to be a topic of primary importance in the discussion on acceptance criteria for risk bearing activities.