This paper investigates the system identification and stability analyses of a turbojet engine in start-up mode. Stability analyses are performed for automatic feedback control algorithm which switches engine from start-up to operational mode. This process requires engine rotational speed and acceleration data which are obtained via extensive engine tests. Those tests are carried out on an altitude testbed at sea level static conditions to obtain above mentioned data with respect to the fuel control command. The process consists of construction of a gain scheduled engine dynamics model and Lyapunov stability analyses. Engine dynamics are described as transfer functions. Mathematical model parameters are identified from test data to perform feasible stability analyses and to define feasible stability regions. The contribution of this study for a turbojet engine is the determination of stability maps in start-up mode and stability region or so-called strip for enabling strategy of the automatic feedback control law. The theoretical results are supported by simulations and an engine test example. Results show that the reference speed of the feedback control algorithm should be NREF ≤ NTJ + 10% for a successful stabilization while switching from start-up to operational mode.