The invention relates to a method of concentrating and eliminating radionuclides in radioactive water from nuclear pools which is based on the capacity of micro-organisms when they are growing to retain radionuclides by forming biofilms on the colonised surfaces. Until now, the inventive method, known as bioremediation, has not been used in the containment area of nuclear power stations. At present, radioactive water in nuclear pools is clarified with a system of demineraliser filters which, when at the end of their working life, generate a considerable amount of radioactive material which has to be managed. The method involving bioremediation, which is performed before the aforementioned filters, prolongs the life of said filters. As a result, there is less radioactive waste to be managed, thereby increasing the profitability of the method.