A fundamental approach to the study of the kinetics of KoRi unit 1 pressurized water nuclear reactor(PWR) systems is developed. This approach treats reactor kinetics problems without consideration of spatial dependence. A dynamic model of the neutron and thermal kinetics of reactor core is formulated, and the causes of reactivities are dealt with in detail. The Tsypkin Locus method is then employed to analyze the stability of the relay actuated control system and to find the conditions for existence of a limit cycle in that system. This relay actuated control system is simulated on the computer to confirm the results of the above stability analysis. Also, the entire reactor control system is simulated to observe the behaviors of the system variables, and some parameters of the Rod Speed Program are optimized to obtain the fastest response by use of the Sequential Simplex direct search method.