A one-dimensional model for the so-called pulsed flames, which are employed for molecular detection and in some combustion related measurements, is formulated and studied numerically. It is shown that the pulsed flame is in fact a highly nonlinear realization of the classical oscillatory instability of the anchored flame. Yet to maintain the pulsed flame within the detector＇s tube one may need an external heat source adapting the pulsations amplitude to the tube length.