  The kinetics of phase and population relaxation in quantum systems induced by
noise with anomalously slowly decaying correlation function P (t) ~ (wt)^{-
alpha}, where 0 < alpha < 1 is analyzed within continuous time random walk
approach. The relaxation kinetics is shown to be anomalously slow. Moreover for
alpha < 1 in the limit of short characteristic time of fluctuations w^{-1} the
kinetics is independent of w. As alpha \to 1 the relaxation regime changes from
the static limit to fluctuation narrowing. Simple analytical expressions are
obtained describing the specific features of the kinetics.
