The paper presents the results of estimates of nuclear-power plant safety based on probabilistic safety analyses and discusses the means used to decrease core damage factors, large release frequency and cancer deaths due to nuclear accidents. Estimates made for new nuclear power plants show that these risks are negligibly small. The radiological effects of the Chernobyl accident are discussed and compared with the negligibly small effects of the TMI-2 accident in the USA in 1978, the only accident with core damage that occurred in pressurized or boiling-water reactors. The accident risks in present and future nuclear-power plants are compared with the accident risks due to other energy sources. Considering the whole fuel cycle, from mineral extraction to waste management, the risks due to nuclear-power accidents are much smaller than the accident risks due to oil, gas or coal fuel cycles. This conclusion is obtained from historical data, taking into account the accidents that have really occurred over the last 40 years, and is confirmed by probabilistic safety analyses for various power industries. (C) 2003 Elsevier Science Ltd. All rights reserved.