Physicists dealing with conventional reactor dynamics recognize two types of instability and reactor behavior beyond the stability region: asymptotic excur sions and nonlinear periodic oscillations. A periodically pulsed reactor (PPR) has another peculiar instability: Under certain conditions, its power tends to oscillate at a frequency just twice less than the reactor pulsation frequency. The PPR dynamics far beyond the stability region are analyzed by using a discrete nonlinear model. A PPR with a negative temperature reactivity effect inevitably shows the chaotic power pulse energy behavior known as “deterministic chaos.” The way by which a reactor goes to chaos is defined by the time de pendence of the feedback and by the kind of dynamics model used. The most usual case is a Feigenbaum transition in which the PPR passes through an infinite cascade of oscillation period doubling before chaotic motion appears. The transition of PPR to random behavior through the Feigenbaum scenario must be considered to be “safe.”