Bulk nanolayered Cu/Nb composites fabricated by accumulative roll bonding (ARB), leading to a nominal layer thickness of 18nm, were subjected to large shear deformation by high-pressure torsion at room temperature. The evolution of the microstructure was characterized using X-ray diffraction, transmission electron microscopy and atom probe tomography. At shear strains of ∼4, the crystallographic texture started to change from the one stabilized by ARB, with a Kurdjumov–Sachs orientation relationship and a dominant {112}Cu||{112}Nb interface plane, toward textures unlike the shear texture of monolithic Cu and Nb. At larger strains, exceeding 10, the initial layered structure was progressively replaced by a three-dimensional Cu–Nb nanocomposite. This structure remained stable with respect to grain size, morphology and global texture from strains of ∼290 to the largest ones used in this study, 5900. The three-dimensional self-organized nanocomposites comprised biconnected Cu-rich and Nb-rich regions, with a remarkably small coexistence length scale, ∼10nm. The results are discussed in the context of the effect of severe plastic deformation and strain path on microstructure and texture stability in highly immiscible alloy systems.