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The quench propagation and the stability of external stabilized and internally stabilized RHQT Nb3Al superconductors were studied experimentally. The Cu to non-Cu ratio of the externally stabilized conductor and the Ag to non-Ag ratio of the internally stabilized conductor are 0.38 and 0.215, respectively. Measurements were made also with a reference conductor where cladded Cu was removed from the externally stabilized conductor and with another reference conductor where Ag cores of the internally stabilized conductor were replaced by Nb3Al. Incorporation of either external or internal stabilizer increases the minimum propagating current. The measured propagation velocities agree with the analytical values. The external stabilization by cladding Cu increases the heater energy required for quench. Either external or internal stabilizer increases the length of normal zone when a certain level of normal voltage appears over the whole sample. It is preferable from the viewpoint of quench protection, because identical Joule heating energy is dissipated in a longer region to reduce the temperature increase at a hot spot.