Site-specific DNA-binding proteins locate their target sites by facilitated diffusion. Several proteins have been shown to slide along DNA in vitro. However, whereas sliding is often envisaged as one-dimensional tracking of the DNA major groove, such a mechanism would not allow linear diffusion over long distances in vivo, where short stretches of free DNA are delimited by bound proteins. I propose a two-dimensional sliding mechanism, in which the protein diffuses freely on the cylindrical DNA surface, and I present experiments that can distinguish between one- and higher-dimensional diffusion along the DNA contour length. At 100 mm NaCl, translocation of EcoRI restriction endonuclease between sites on two DNA helices connected by a Holliday junction is as efficient as between sites on the same helix, indicating a three-dimensional mechanism. At 25 mm NaCl, translocation between sites on the same DNA helix is more efficient, indicating a role for sliding at low ionic strength. Obstacles attached to the major groove of one face of the DNA helix did not interfere with sliding, regardless of their orientation relative to the cleavage sites. This result is compatible with two-dimensional but not one-dimensional sliding. As illustrated by Monte-Carlo simulation, two-dimensional sliding may not only allow proteins to move around nucleosomes in vivo but also reduce the redundancy of their search for the target site.