Dephasing due to nonstationary 1/f noise

4 pages, 2 figures, to be published in the proceedings of the Vth Rencontres de Moriond in Mesoscopic PhysicsInternational audienceMotivated by recent experiments with Josephson qubits we propose a new phenomenological model for 1/f noise due to collective excitations of interacting defects in the qubit\'s environment. At very low temperatures the effective dynamics of these collective modes are very slow leading to pronounced non-Gaussian features and nonstationarity of the noise. We analyze the influence of this noise on the dynamics of a qubit in various regimes and at different operation points. Remarkable predictions are absolute time dependences of a critical coupling and of dephasing in the strong coupling regime