Analytical methods of nonlinear dynamics and numerical simulations for the coupling equations of Navier-Stokes and flight mechanics are used to study the dynamic behaviour of pitching motions of reentry capsules with the variation of Mach number, and rocking motions of swept wings with the variation of angle of attack. Conditions under which the dynamic instability, Hopf bifurcation and saddle-node bifurcation occur are obtained. The node-saddle-node topological structure in the phase portrait, I.e. The state of bi-attractors (attracting basins) is described. The evolving process of dynamic behaviour and flow fields are given. The theories are compared with some numerical simulations conducted by the authors. Besides, some verifiable experimental results are cited. The agreement between them is very well.