We have investigated the dependence of the rate of cleavage of DNA by EcoRI, HindIII, and BamHI on the chain length of the substrate. In order to keep the influence of flanking sequences and of nonspecific binding identical for all substrates we have carried out all experiments with the same plasmid DNA which had been digested previously with a variety of different restriction enzymes to give a set of substrates of different lengths. Our results show that depending on the buffer conditions long substrates are cleaved faster than small ones. We interpret these findings to mean that under certain conditions a linear diffusion of the enzymes on the DNA is involved in localizing the recognition sites. For EcoRI the mean diffusion length is approximately 1000 base pairs at 1 mM MgC12 which can be shown by diffusion theory to correspond to a linear diffusion coefficient of 5 X 10(-10) cm2 s-1. At 10 mM MgCl2 the linear diffusion of EcoRI is negligible and does not lead to a significant enhancement of the rate of site localization. In the presence of nonsaturating amounts of one of the prokaryotic histone-like protein Hu (NS 2) small and large DNA substrate are cleaved with identical rate by EcoRI indicating that other proteins bound to the DNA constitute a barrier across which linear diffusion cannot take place. We conclude that linear diffusion, albeit detectable under certain conditions in vitro, probably is of little importance for the process of site localization in vivo.