Pressure extinction limits of non-premixed (diffusion) flames are studied theoretically by examining the two key non-dimensional parameters: Damkohler number and radiationheat-loss parameter. It is found that there is a critical value of the reaction order, n cr , for a given flame and flow configuration. If the overall combustion reaction order n is less than n cr , a high-pressure flame extinction limit exists as a result of a small limiting Damkohler number. If the overall combustion reaction order n is greater than n cr , both heat loss and Damkohler number contribute to the existence of the low-pressure extinction limit. The contribution of the Damkohler number increases with flame intensity. Since the value of the critical reaction order n cr varies with flame configuration and flow type, three examples of diffusion flames adjacent to a condensed fuel are given in the paper: stagnation-point flame, side-stabilised flame and spherical flame. The reason for the different value of the critical n cr is due to the different pressure dependence of the flow residence time in the flame stabilisation zone of these flames.