Abstract: A stage by stage mathematical model of the compressor in a turbojet engine is developed based on the control volume theory. The characteristic relationship is applied to solve the governing equations of mass, momentum and energy for each control volume. The stage forces and shaft work required to solve equations are derived from a set of steady stage performance. A first order lagging equation is used to acount for dynamic effects. This model can simulate the compressor response to inlet temperature transients and find the critical stage. It is shown from the results that the inlet temperature rise just prior to system instability is approximately linear with the inlet temperature ramp rate.