A nonlinear model, FLASHOVER A1, is presented within a zonal formulation which may be used to predict the geometrical and thermo-physical conditions which lead to an instability in the system. In particular, the existence of a critical fire radius is demonstrated at which the state becomes unstable. After this point a rapid development to a post-flashover state would be expected, given sufficient fuel and ventilation. In a practical case it would be desirable to attempt to ensure that the fire radius remains below the critical value. In such a way this model may assist in the assessment of a design.