Nonstationary dynamics has been observed in very‐low‐frequency (10−2–10−1Hz) ac susceptibility and noise measurements on the thiospinel CdCr1.7In0.3S4spin glass. The time relaxation of the ac susceptibility yields a large decrease of the out‐of‐phase component &khgr;‘towards a finite stationary value. The relaxation of the spectral density of the magnetization derived from zero‐field noise measurements is in remarkable agreement with the behavior of &khgr;‘. The observed time dependence compares well with the predictions from the thermoremanent magnetization decay analyses. In the range of times of &khgr;‘measurements, the linear‐response theory applies to the nonstationary dynamics.