The potential for processive EcoRI endonuclease hydrolysis has been examined on several DNA substrates containing two EcoRI sites which were embedded in identical sequence environments. With a 388-base pair circular DNA, in which the two recognition sites are separated by 51 base pairs (shorter distance) or 337 base pairs (longer distance), 77 and 34% of all events involved processive hydrolysis at ionic strengths of 0.059 and 0.13, respectively. However, the frequency of processive action on linear substrates, in which the two sites were separated by 51 base pairs, was only 42 and 17% at these ionic strengths, values half those observed with the circular DNA. Processive action was not detectable on circular or linear substrates at an ionic strength of 0.23. These findings indicate that DNA search by the endonuclease occurs by facilitated diffusion, a mechanism in which the protein locates and leaves its recognition sequence by interacting with nonspecific DNA sites. We suggest that processivity on linear substrates is limited to values half that for small circles due to partitioning of the enzyme between the two products generated by cleavage of a linear molecule. Given such topological effects, measured processivity values imply that the endonuclease can diffuse within a DNA domain to locate and recognize an EcoRI site 50 to 300 base pairs distant from an initial binding site, with minimum search efficiencies being 80 and 30% at ionic strengths of 0.059 and 0.13, respectively. The high efficiency of processive action indicates that a positionally correlated mode of search plays a major role in facilitated diffusion in this system under such conditions. Also consistent with this view was the identification of a striking position effect when two closely spaced EcoRI sites were asymmetrically positioned near the end of a linear DNA. The endonuclease displays a substantial preference for the more centrally located recognition sequence. This preference does not reflect differential sensitivity of the two sites to cleavage per se, but can be simply explained by preferential entry of the enzyme via the larger nonspecific target available to the more centrally positioned recognition sequence. These conclusions differ from those of a previous qualitative analysis of endonuclease processivity over short distances (Langowski, J., Alves, J., Pingoud, A., and Maass, G. (1983) Nucleic Acids Res. 11, 501-513).