Abstract: Natural processes with long-term memory require a mathematical description with fractal (power-law) statistics. Two classes of such discrete processes that are of potential interest to the defence community are the fractal point process and the fractal rate point process. An analysis of fatality data from the conflicts in Afghanistan and Iraq is presented in this paper. The results reinforce the notion that there is a fundamental difference between the two conflicts, with the fatalities in Afghanistan behaving as a typical fractal point process with intermediate intermittency, while the fatalities in Iraq correspond to a fractal rate point process. These findings are supplemented by calculations of intermittency for several combat simulations. Implications of the results for the critical behaviour of the two systems, as well as future directions in terms of intermittency in models, are discussed.