Dephasing in disordered metals with superconductive grains

Temperature dependence of electron dephasing time $\tau_\phi(T)$ is calculated for a disordered metal with small concentration of superconductive grains. Above the macroscopic superconducting transition line, when electrons in the metal are normal, Andreev reflection from the grains leads to a nearly temperature-independent contribution to the dephasing rate. In a broad temperature range $1/\tau_phi(T)$ strongly exceeds the prediction of the classical theory of dephasing in normal disordered conductors, whereas magnetoresistance is dominated (in two dimensions) by the Maki-Tompson correction and is positive.