Supersonic air intakes are of major importance for the efficient operation of aircraft engines. Meanwhile, shock waves formed in the intake are very sensitive to small perturbations. This work addresses the flow behavior in an intake whose upper and lower walls are 9 degrees bent. Solutions of the unsteady Reynolds-averaged Navier-Stokes equations are obtained with an ANSYS CFX finite-volume solver. Numerical simulations reveal a hysteresis of shock wave locations under gradual variations of the inflow Mach number or pressure given at the exit. At the ends of the hysteresis bands, there are abrupt changes in the flow field. The changes are associated with a swallowing of the shock wave or its expulsion from the channel. The existence of hysteresis means the non-uniqueness of flow regimes in the intake. This implies different losses of the total pressure and different thrusts of an air breathing engine in the same flight conditions.