This paper identifies the mechanisms of phase and structural transformations during severe plastic deformation by shearing under pressure (high-pressure torsion) of an Al-Zn-Mg-Fe-Ni-based aluminum alloy depending on different initial states of the material (an ingot after homogenizing annealing and a rod produced by radial-shear rolling). Scanning and transmission electron microscopy are used to determine the morphological and size characteristics of the structural constituents of the alloy after high-pressure torsion. It has been found that, irrespective of the history under high-pressure torsion, fragmentation and dynamic recrystallization results in a nanostructural alloy with a high microhardness of 2000 to 2600 MPa. Combined deformation processing (high-pressure torsion + radial-shear rolling) is shown to yield a nanocomposite reinforced with dispersed intermetallic phases of different origins, namely Al₉ FeNi eutectic aluminides and MgZn₂, Al₂ Mg₃ Zn₃, and Al₃ Zr secondary phases. The results of uniaxial tensile testing demonstrate good mechanical properties of the composite (ultimate tensile strength of 640 MPa, tensile yield strength of 628 MPa, and elongation of 5%).