Results of experimental studies of the afterburning of the exhausts of highly boron-loaded, fuel-rich propellants with air and results of boron single particle combustion studies have been examined for definition of limiting processes causing incomplete combustion of boron in typical afterburners, particularly at low afterburner pressure. This examination indicates that ignition of the boron particles, inhibited by the presence of a coating of boron oxide, is likely the controlling process. Transient differential equations describing the generation and removal of oxide and the temperature history of a particle have been derived, converted to difference equation form and programmed for computer solution to permit prediction of whether or not a given particle will ignite and, if it will, the time required for ignition. Predicted ignition times for particles studied by Macek in a flat-flame burner have been compared with his experimental results—reasonably good agreement has been obtained. The program has been used to predict effects of initial boron oxidethickness,particlesize,oxygen partial pressure, initial particle temperature, ambient lemperature, and effective surroundings radiation temperature on ignition time. One important result is the prediction of increased ignition time with decreasing oxygen partial pressure, a result consistent with the observation of low afterburner efficiency at low afterburner pressure.