It is necessary to clarify the nature of secondary ignition of condensed fuels, in particular in order to develop methods for reliable suppression of fires. To study the mechanism of the near-limit oscillatory combustion regime experiments were performed with equipment similar to that used to determine the oxygen index of polymers at a gas mixture flow rate of 1 cm/sec. A polymethyl methacrylate specimen was ignited from above in airflow which was terminated when combustion had reached a steady-state regime, at which point a nitrogen-oxygen mixture with 14% volume oxygen concentration was supplied through an electrically controlled valve. A kinogram is presented which clarifies several features of the secondary ignition observed in the final stage of flame oscillation. The authors evaluate the possible reduction in temperature of the surface of the solid phase over the ignition delay time. With consideration of gas formation and heat loss by radiation, the decrease in temperature of the pyrolysis zone surface after disappearance of the flame is obviously greater.