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The authors simulated spreading of solid copper (Cu) and gold (Au) nanoparticles (5–7 nm size) on the (100) face of the same metal by using molecular dynamics. Then, the results obtained for the copper (nanoparticle)/copper (substrate) system were qualitatively compared to some available experimental data on the spreading of copper microparticles (5–20 μm) on the surface of polycrystalline copper. Before simulating the nanoparticle spreading, the size dependence of the melting temperature was investigated for copper and gold nanoparticles. When temperatures were by 25–35 K lower than the copper particle melting temperature, the observed value 40° of the equilibrium contact angle qualitatively agreed with the range 20–25° that the authors evaluated using an experimental snapshot of a copper microparticle on the copper polycrystalline substrate at temperature by 33 K lower than the bulk copper melting point. However, the characteristic spreading times 0·5–10 ns found for nanoparticles in computer experiments differ from that for copper microparticles (3 h ≈ 105 s) by many orders of magnitude. The characteristic times of spreading for copper and gold nanoparticles were also estimated by using the capillary-induced surface diffusion concept, the similarity theory and an available experimental value of the spreading duration for solid copper microparticles. The theoretical estimations in question satisfactorily agree with the authors’ molecular dynamics results.