  We study decoherence due to low frequency noise in Josephson qubits.
Non-Markovian classical noise due to switching impurities determines
inhomogeneous broadening of the signal. The theory is extended to include
effects of high-frequency quantum noise, due to impurities or to the
electromagnetic environment. The interplay of slow noise with intrinsically
non-gaussian noise sources may explain the rich physics observed in the
spectroscopy and in the dynamics of charge based devices.
