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The dynamics of high energy runaway electrons is analyzed for plasmas with high impurity content. It is shown that modified collision terms are required in order to account for the collisions of the relativistic runaway electrons with partially stripped impurity ions, including the effect of the collisions with free and bound electrons, as well as the scattering by the full nuclear and the electron-shielded ion charge. The effect of the impurities on the avalanche runaway growth rate is discussed. The results are applied, for illustration, to the interpretation of the runaway electron behavior during disruptions, where large amounts of impurities are expected, particularly during disruption mitigation by massive gas injection. The consequences for the electron synchrotron radiation losses and the resulting runaway electron dynamics are also analyzed.