Red blood cell velocity and diameter were measured in vessels of the wing of the unanesthetized bat (Myotis lucifugus) from the supplying artery to the capillaries. These data were used to determine the manner in which velocity, shear rate, volume flow, and blood pressure depend on the vessel's hierarchical position within the vascular network. The results show that velocity decreases in an almost linear fashion as the capillary is approached but that the shear rate increases as one progresses distally from the supplying artery. Blood volume flow was found to decrease as an exponential function of the branching order. Comparison with available date in some animal species, including man, indicates some agreement in capillary velocity, although significantly lower values have been reported in some preparations. Using a method whereby blood pressure distribution could be obtained from anatomical data and center-line blood velocity, the rheologic alterations accompanying consecutive vessel branching were deduced and found to be in good agreement with data available in the literature.