[en] By operational experience of nuclear power plants and realize dlevel of availability of plant, systems and componenst reliabiliuty, operational safety and public protection, as a source on nature of distrurbances in power plant systems and lessons drawn by the TMI-2, in th epaper are discussed: examination of design safety for ultimate ensuring of safe operational conditions of the nuclear power plant; significance of the adequate action for keeping proess parameters in prescribed limits and reactor cooling rquirements; developed systems for measurements detection and monitoring all critical parameters in the nuclear steam supply system; contents of theoretical investigation and mathematical modeling of the physical phenomena and process in nuclear power plant system and components as software, supporting for ensuring of operational safety and new access in staff education process; program and progress of the investigation of some physical phenomena and mathematical modeling of nuclear plant transients, prepared at faculty of mechanical Engineering in Belgrade. (author)