The possibility of formation of a nanocrystalline structure (with a grain size smaller than 100 nm) in four Al-Mg-Sc alloys with 3.1–5.9% Mg during severe plastic deformation by torsion at a hydrostatic pressure of 6 GPa (high-pressure torsion (HPT)) has been studied. Room-temperature HPT of the alloys is shown to produce a nanocrystalline structure if the magnesium content is more than 4% (in the range 0.16–0.31% Sc). As the magnesium content increases, the grain size decreases and is minimal (40–50 nm) in a 01570 alloy with 5.9% Mg and 0.3% Sc. The structure of the HPT-processed 01570 alloy remains nanocrystalline upon heating to 200°C or at a deformation temperature as high as 200°C. Postdeformation heating is found to cause aging processes. The hardening of all the Al-Mg-Sc alloys is maximal after HPT at 20°C followed by aging at 300°C.