Hypersonic airbreathing propulsion is one of the top techniques for future aerospace flight, but there are still no practical engines after seventy years' development. Two critical issues are identified to be the barriers for the ramjet-based engine that has been taken as the most potential concept of the hypersonic propulsion for decades. One issue is the upstream-traveling shock wave that develops from spontaneous waves resulting from continuous heat releases in combustors and can induce unsteady combustion that may lead to engine surging during scramjet engine operation. The other is the scramjet combustion mode that cannot satisfy thrust needs of hypersonic vehicles since its thermos-efficiency decreases as the flight Mach number increases. The two criteria are pro-posed for the ramjet-based hypersonic propulsion to identify combustion modes and avoid thermal choking. A standing oblique detonation ramjet (Sodramjet) engine concept is proposed based on the criteria by replacing diffusive combustion with an oblique detonation that is a unique pressure-gain phenomenon in nature. The Sodramjet engine model is developed with several flow control techniques, and tested successfully with the hypersonic flight-duplicated shock tunnel. The experimental data show that the Sodramjet engine model works steadily, and an oblique det-onation can be made stationary in the engine combustor and is controllable. This research demon-strates the Sodramjet engine is a promising concept and can be operated stably with high thermal efficiency at hypersonic flow conditions.