The invention relates to a reactor with a system or systems for controlling the regulation and the cutoff of a power output on the basis of neutron absorption using motile neutron absorber bodies. The invention also relates to a method of regulating the output of a nuclear reactor, and to absorber bodies that are adapted to the method and to a regulating system. According to the invention, spherical absorber bodies such as SAS are used in guides in the reflector in such an arrangement that a maximum neutron absorption is achieved adjacent to areas of a maximum output of the core and a reduced or zerovalent absorption in areas where the output of the core is reduced.