Abstract: In hypersonic boundary layer, the first mode and the second mode are the main unstable modes which related to the boundary layer transition. In addition to these unstable modes, there is also a type of stable mode. At the leading edge, the phase speed of this stable mode is close to the phase speed of fast acoustic, so it is called fast mode. In the process of receptivity, it plays an important role of exciting unstable modes in boundary layer. Leading edge receptivity theory explains the mechanism of exciting the first mode. For hypersonic boundary layer, the similar solution is used as the basic flow, and the behavior of fast mode and slow mode are researched using linear stability theory and direct numerical simulation. The results indicate the location of the mode exchange is related to mach number. According to the results of linear stability theory, the critical frequency is defined. If the frequency of the disturbance is larger than the critical frequency, the first mode and the second mode are in the same branch; while the frequency of the disturbance is smaller than the critical frequency, the first mode and conjugate mode of the second mode are in the same branch. With the help of adjoint equations of linear stability equations, numerical results are analyzed. Numerical results indicate that when the fast and slow modes go though the region of second mode, they will evolve into the second mode. It can be explained by the propagation of the mode in the nonparallel flow.