Abstract: We analyze recent experimental data on the complex inductance of dc SQUIDs that show 1/f inductance noise that is highly correlated with conventional 1/f flux noise. We argue that there are two mechanisms likely to give rise to the observed inductance noise: fluctuations in the kinetic inductance of superconducting wires caused by the dynamics of scattering centers; and the dynamics of unpaired spins of electrons localized on or close to the surface of the superconducting wires. We analyze both possibilities in detail and conclude that the latter is likely to be dominating in the experiments. Moreover, we argue that the experimental data imply a formation of long range order in fractal spin structures on the surface of the superconducting wiring. We show that such structures appear naturally in a random system of spins with wide distribution of spin-spin interactions. We perform numerical simulations on the simplest model of this type and show that it exhibits 1 / f1 + ζ magnetization noise with small exponent ζ and reproduces the correlated behavior observed experimentally.