Bifurcation theory has been used to study the nonlinear dynamics and stability of many modern aircraft, especially in broad angle-of-attack flight dynamics. However, the main application of bifurcation analysis is based on numerical simulations to predict and explain the nonlinear instability of flight dynamics by the use of parametric continuation methods. Bifurcation theory is applied to theoretically analyze the nonlinear phenomena of longitudinal flight dynamics, by the choice of the elevator deflection and mass of the aircraft as system parameters. Both stationary and Hopf bifurcations may appear at some critical values of elevator command. Discontinuity also may occur at system equilibria as system parameters vary. The bifurcation phenomena occurring in nonlinear aircraft dynamics might result in jump behaviors, pitch oscillations, or system instabilities. Numerical study of a simple third-order model of longitudinal dynamics verifies the theoretical analysis. Qualitative results are obtained to understand the longitudinal flight dynamics.