Critical conditions are obtained for ignition in a self-heating solid system consisting of two components generating heat independently, one component being inexhaustible and the other exhaustible by either simple first order or autocatalytic reaction. Ignition depends on whether the exhaustible component can cause a temperature rise in exess of the upper stationary, but unstable, value possible for the inexhaustible component reacting alone. The system provides a theroretical model for some commonly occurring examples of self-heating and ignition in porous solids containing oxidizable oils.