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Metallic nanocomposites with high strength and extensive plasticity have attracted intensive scientific interest. Herein, molecular dynamics simulations are performed to explore the mechanical responses of bicontinuous Cu/Ni nanocomposites with a representative isotropic gyroidal architecture. The effect of volume fraction of constitute phase on the mechanical properties is discussed. Tensile results show that Cu/Ni interface acts as a barrier to dislocation propagation, causing the dislocation activity of nanocomposite occurring in the individual matrixes. The dislocation activity is more pronounced in the soft Cu phase and the crack propagates in Cu matrix rather than along the Cu/Ni interface, resulting in the breakage of material occurring in Cu phase for all nanocomposites. After the failure of Cu matrix, the remaining Ni matrix can still bear the applied load alone. The modulus and strength of Cu/Ni nanocomposites are higher than those of individual constitute phases and even the sum of two matrixes. Similar to nanoporous materials, Cu/Ni nanocomposites obey the power relations between mechanical properties and volume fraction. The research further gives an atomic insight into the mechanical responses and associated deformation mechanisms of metallic bicontinuous nanocomposites.