The interaction of impurity atoms of light elements C, N, O with self-interstitials in fcc metals Ni, Ag and Al was studied by the molecular dynamics method. It is shown that the self-interstitial atom in fcc metals migrates through at least two mechanisms: by the displacement and rotation of the <100> dumbbell and by the crowdion mechanism. The first mechanism is characterized by broken trajectories of atomic displacements, the second-by straight ones along close-packed directions in the crystal. The binding energies of impurity atoms with self-interstitials in Ni, Ag and Al have been calculated. It is shown that impurity atoms are effective "traps" for interstitial atoms that migrate relatively quickly in a crystal. When a self-interstitial atom and an impurity atom interact, the interstitial atom forms a dumbbell configuration with the axis along the <100> direction, and the impurity atom is located in the nearest octahedral pore. To analyze the effect of impurities on the diffusion mobility of interstitial atoms, we calculated the activation energy of migration of the interstitial atom in pure metals and metals containing 10 % of impurity atoms. It was found that the mobility of interstitial atoms is significantly reduced due to the presence of impurities in the metal. At the same time, the contribution of the crowdion mechanism also decreased.