Bundles of capillaries, each supplied by a distinct arteriole, are arranged within skeletal muscle to form a vascular bed. If the arteriole end of one of these capillary bundles is adjacent to the arteriole end of an adjacent bundle, then perfect co-current exchange will occur between two groups of capillaries. This exchange is due to the differences in velocities of blood in the capillaries of the two bundles or in the oxygen concentration of the blood at the arterial end of the capillaries of the two bundles. Considerable diffusion between these adjacent groups can be expected to occur. If the arteriole end of one of these bundles is adjacent to the venous end of the adjacent bundle, then perfect counter-current exchange occurs between these two groups of capillaries. There is a considerable diffusion between these adjacent groups due to the fact that oxygen in the richly perfused arterial end of one group diffuses into the adjacent poorly perfused region at the venous end of the other group. This interaction occurs even if all the capillaries have the same blood flow velocity and initial concentration. The situations concerning perfect co-current and perfect counter-current flows in adjacent capillaries have been solved. These situations are ideal and in reality in the skeletal muscle, neither of them occurs; instead the arterial end of one capillary bundle is located between the arterial and venous ends of an adjacent bundle. Our main task (which has never been examined before) is to examine the case where the capillaries are staggered in such a way that the arterial ends of one bundle are not aligned with either the arterial or the venous   end of the adjacent bundle. Such an orientation is most commonly observed within skeletal muscle.