Nanostructured metals and alloys possess ultrahigh strength but suffer from severe shear instability (strain localization). Recent experiments have shown that the strength and strain delocalization capability of some novel nanostructured alloys and nanolayered composites can be enhanced simultaneously by introducing nanoscale amorphous interfacial layers. However, the study on the underlying mechanism is still in an embryonic stage due to the ignorance of the complicated elemental composition of the interfacial layers, especially the compositional gradient along the interface thickness. Here, the atomic mechanisms of the tensile deformation of Cu/Nb nanolayered composites with amorphous interfacial layers are systematically investigated by molecular dynamics simulations. Depending on whether the composition of the interfacial layers is invariable or has a gradient distribution along the interface thickness, these samples are classified as amorphous or gradient samples, respectively. The simulations of normal Cu/Nb nanolayered composites with ordinary incoherent Cu‒Nb interfaces are also included for comparison, the results of which show that strain localization occurs due to the inhomogeneous plastic deformation between soft and hard grains in the Cu and Nb layers. The strain localization is inhibited in the amorphous samples mainly through the activation of deformation twinning in the Cu and Nb layers that produces a co-deformation between grains. Intriguingly, the gradient arrangement of the elemental composition of the amorphous interfacial layers gives a further stronger strain delocalization by further promoting the co-deformation between grains through stimulating more nanotwins in Cu layers and hindering twin growth in Nb layers, and by producing a much more uniform von Mises strain distribution in the interfacial layers. In addition, a better strain delocalization capability can be obtained when the thickness of the interfacial layers is closer to that of the crystalline ones in the amorphous sample or the range of gradient composition is larger in the gradient one.