[en] The idea about the equivalency or differences in mechanisms of action of low to very low doses, or dose rates of noxious environmental factors vs high doses/dose rates belongs for long time to the controversial questions in ecophysiology, incl. radioecology. Numerous observations of stimulatory actions of otherwise noxious environmental factors, as heavy metals, poisons, UV- and ionizing radiation, heat shock, starvation, etc. are documented since the 19^th century. These phenomena were overall denoted as 'hormesis'. The opinions on the effects of low dose rates of ionizing radiation of natural or artificial origin are changed in broad range since the discovery of x-rays up to present time, from uncritical acceptance of the conception of its beneficial effects to the total denial of this alternative. The arguments pro and contra, however, were based often not on objective scientific knowledge, but rooted in conjecturally political, economical and ideological approaches. In present time, the so called 'linear no-threshold' model is prevailing in most of theoretical works and practical applications on the field of radioecology and environmental protection, as well. This model do not admit any beneficial effects of low radiation doses. It grants on one side, that no potential danger corresponding to given level of the noxious factor will be underestimated, but, on other side, do not considers the inherited defensive and adaptive capabilities of living organisms, including humans, to adapt to often extremely conditions (e.g. survival at high or low temperatures, at the lack of oxygen, in dehydration, at high salinity, etc.), acquired during the long-lasting evolution. The aim of our contribution was to evaluate the current state of scientific discussion on the radiation hormesis, to point out the possible mechanisms of the positive effects of low doses of radiation on the living organisms and to discuss some challenges in uncritical and mechanistic use of the TNT-model in radiation safety. (author)