In a countercurrent flow reactor (CFR) the reactants flow countercurrently at equal velocities and flow rates through two compartments, with negligible heat transfer resistance between the two sections. Under an intermediate level of cooling capacity, the ignited steady state may become unstable leading to formation of period-n or aperiodic states. The temporal temperature profiles of all the states with complex dynamics have two temperature peaks (pulses) that due to the countercurrent flow move in opposite directions. Eventually, one pulse is extinguished and a new one is generated by backfiring from the second moving pulse. Usually, some backfired pulses are extinguished before reaching a reactor exit. Thus, the conditions next to the reactor exit are not sufficient for classification of the motion. The best characterization of the dynamic motion is by construction of the space-time dependence of the temperature or concentration. Various period-n states exist within narrow parameter windows within the region of chaotic states. For all states with complex dynamics the time average of rate of heat removal by cooling through the wall is either equal or exceeds that of the convective heat removal by the effluents.