This work investigates the self-excited spanwise homogeneous perturbations arising in a shock-wave/boundary-layer interaction (SWBLI) system formed in a hypersonic flow of molecular nitrogen over a double wedge using the kinetic Direct Simulation Monte Carlo (DSMC) method. The flow has a Knudsen and unit Reynolds numbers of 3.4 × 10−3 and 5.2 × 105 m−1, respectively. Strong thermal nonequilibrium exists downstream of the Mach 7 detached (bow) shock generated due to the upper wedge surface. Global linear instability mechanisms are expected to make the pre-computed 2-D base flow potentially unstable under self-excited, spanwise periodic perturbations. Goertler-type vortices are also expected to form due to curved streamlines in the presence of a strong recirculation region. Our specific intent is to assess the growth rates of unstable modes, the wavelength, location, and the origin of spanwise periodic flow structures, and the characteristic frequencies present in this interaction.