There is much interest in the recent years in the nanoscale metallic multilayered composite materials due to their unusual mechanical properties, such as very high flow strength and stable plastic flow to large strains. These unique mechanical properties have been proposed to result from the interface-dominated plasticity mechanisms in nanoscale composite materials. Studying how the dislocation configurations and densities evolve during deformation will be crucial in understanding the yield, work hardening, and recovery mechanisms in the nanolayered materials. In an effort to shed light on these topics, uniaxial compression experiments on nanoscale Cu/Nb single-crystal multilayer pillars using ex situ synchrotron-based Laue x-ray microdiffraction technique were conducted. Using this approach, we studied the nanoscale Cu/Nb multilayer pillars before and after uniaxial compression to about 14% of plastic strain and found significant Laue peak broadening in the Cu phase, which indicates storage of statistically stored dislocations, while no significant Laue peak broadening was observed in the Nb phase in the nanoscale multilayers. These observations suggest that at 14% plastic strain of the nanolayered pillars, the deformation was dominated by plasticity in the Cu nanolayers and elasticity or possibly a zero net plasticity (due to the possibility of annihilation of interface dislocations) in the Nb nanolayers.