The phenomenon of hormesis, i.e. beneficial effect of low dose irradiation is up to now under discussion. The existence of this phenomenon contradicts to the ″linear hypothesis″ which considers as harmful even minute radiation doses. Effects of radiation should subject to the principle of Paracelsius that only dose determines the toxicity of a substance. Data on cancer incidence among survivors of Hiroshima and Nagasaki bombardments, and inhabitants of near Chernobyl regions are discussed. The epidemiology of cancer among inhabitants of the Earth regions with a high natural radiation level do not support the ″linear hypothesis″. The adoption of the harmlessness of low doses seems to be very important for development of reasonable hygienic standards for the work with sources of radiation.