The influence of paramagnetic impurities on the thermodynamic properties of two‐band superconductors at zero and near zero temperatures is investigated. It is shown that due to interband scattering of electrons there is one gap in two‐band superconductors with impurities. The extreme cases of low and large impurity concentrations are investigated. In the first limiting case an increase in the concentration is accompanied by a linear decrease of order parameters. The expression for the energy gap, densities of states near the energy gap, and the specific heat as functions of impurity concentration are given. Copyright © 1969 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim