Abstract: Fluctuations of the qubit frequencies are one the major problems to overcome on the way to scalable quantum computers. Of particular importance are fluctuations with the correlation time that exceeds the decoherence time due to decay and dephasing by fast processes. The statistics of the fluctuations can be characterized by measuring the correlators of the outcomes of periodically repeated Ramsey measurements. This work suggests a method that allows describing qubit dynamics during repeated measurements in the presence of evolving noise. It made it possible, in particular, to evaluate the two-time correlator for the noise from two-level systems and obtain two- and three-time correlators for a Gaussian noise. The explicit expressions for the correlators are compared with simulations. A significant difference of the three-time correlators of the noise from two-level systems and from a Gaussian noise is demonstrated. A strong broadening of the distribution of outcomes of Ramsey measurements, with a possible fine structure, is found for the data acquisition time comparable to the noise correlation time. Work of Mark Dykman, Filip Wudarski, Yaxing Zhang, Alexander Korotkov, and A. G. Petukhov