A brief description of some of the non-Newtonian flow phenomena encountered in the flow of biological fluids. Primary emphasis is on the interaction among shear-dependent and scale-dependent effects that occurs when the flow is slow and the tube small. Non-Newtonian fluid models are discussed and the experimental data for the pressure drop and velocity distribution of blood flow in small tubes are reviewed. A transformation parameter is described that stretches the radial dimension in such a way that the velocity distribution directly indicates the viscosity variation across the flow. Simple analytic models are described that reproduce many features of the experiments. (Invited lecture, 1970 International Seminar on Heat and Mass Transfer in Rheologically Complex Fluids.) (See also R-767, R-768, RM-6214.) 43 pp. Ref.