We investigate the influence of nonstationary 1/fμ noise, produced by interacting defects, on a quantum two-level system. Adopting a simple phenomenological model for this noise we describe exactly the corresponding dephasing in various regimes. The nonstationarity and pronounced non-Gaussian features of this noise induce new anomalous dephasing scenarii. Beyond a history-dependent critical coupling strength, the dephasing time exhibits a strong dependence on the age of the noise and the decay of coherence is not exponential.