The stability and bifurcations of a nonlinear flight system with time delay are investigated. Firstly, considering
the time delay in measurement of angle of attack, a polynomial differential system with time delay for aircraft longitudinal
motion is suggested. Then by applying Hopf bifurcation and center manifold theories of functional differential equations, the
stability and bifurcations of the time-delayed system are studied analytically, and existence conditions for Hopf bifurcations
as well as formulas for calculating bifurcation points and stability of the bifurcation limit cycle are derived. Finally, the
theoretical conclusions are applied to analyze a practical example of high angle-of-attack flight. The results show that the
delay in the measurement of angle of attack can cause instability, moreover, the Hopf bifurcation occurs and the periodic
oscillation of longitudinal direction arises when the measurement delay exceeds the critical value. The conclusion has the
reference significance in practice.