We develop a technique to compute high-frequency asymptotics of spin correlators in weakly interacting disordered spin systems. We show that the high frequency spin correlators decreases exponentially at high frequencies, <S S> ~ exp(-omega t*) and compute the characteristic time, t*, of this dependence. In a typical disordered system a significant number of spins have a strongly coupled neighbor. We show that this, together with the exponential decrease of the spin correlator at high frequencies translates into a low-frequency 1/f noise in all physical quantities sensitive to the spin state of the strongly coupled pairs. We discuss the application of these results to the problem of susceptibility and flux noise in superconducting circuits. Work in collaboration with Lev Ioffe and Alexei Kitaev.