Abstract
We discuss the combined effect of spin delocalization and one-dimensional (1D) diffusion on the hyperfine-controlled nuclear relaxation and EPR linewidth. We calculate the local-spin-correlation functions in the 1D random-walk model for a particle delocalized over several sites. At low frequency the divergent diffusive contribution is independent of the delocalization; however, the delocalization introduces a negative frequency-independent contribution which is proportional to the delocalization length.