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Nano-indentation hardness as a function of bilayer period has been measured for sputter-deposited Cu–Nb multilayers. For this face-centered cubic/body-centered cubic system with incoherent interfaces, we develop dislocation models for the multilayer flow strength as a function of length scale from greater than a micrometer to less than a nanometer. A dislocation pile-up-based Hall–Petch model is found applicable at the sub-micrometer length scales and the Hall–Petch slope is used to estimate the peak strength of the multilayers. At the few to a few tens of nanometers length scales, confined layer slip of single dislocations is treated as the operative mechanism. The effects of dislocation core spreading along the interface, interface stress and interface dislocation arrays on the confined layer slip stress are incorporated in the model to correctly predict the strength increase with decreasing layer thickness. At layer …