Low shear (γ̇=1 s−1) and shear rate dependent (1 s−1<γ̇<100 s−1) viscosity measurements on aqueous suspensions of rodlike FD-virus particles (length=880 nm, diameter=9 nm) below and above the overlap concentration c* =1 particle/length3 are presented. Properties like intrinsic viscosity [η], the virus concentration and shear rate dependence of η are studied in deionized (‘‘saltfree’’) suspensions and in the presence of NaCl, where the Coulomb interaction between the particles is totally screened. In the latter case, [η] is in excellent agreement with theoretical predictions [A. R. Altenberger and J. S. Dahler, Macromolecules 18, 1700 (1985); R. M. Davis and W. B. Russel, Macromolecules 20, 518 (1987)]. As a function of the virus concentration, η follows certain power laws in c. The observed exponents depend here on the applied shear rate. In the low shear region, η(c) can be described by the well known Huggins behavior. An attempt to fit the data by the popular stretched exponential form failed. The variation of η with shear rate is compared with available theories [M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986); A. R. Altenberger and J. S. Dahler, Macromolecules 18, 1700 (1985); J. S. Dahler, S. Fesciyan, and N. Xystris, Macromolecules 16, 1673 (1983)]. A theory of Hess [Z. Naturforsch. Teil A 35, 915 (1980)] allows us to evaluate the concentration dependent values of the rotational diffusion constant Drot from the η(γ̇) data which are found to be in very good agreement with the values of Drot, obtained by electric or magnetic birefringence [H. Kramer, M. Deggelmann, C. Graf, M. Hagenbüchle, C. Johner, and R. Weber, Macromolecules 25, 4325 (1992); J. F. Maguire and J. P. McTague, Phys. Rev. Lett. 45, 1891 (1980); H. Nakamura and K. Okano, Phys. Rev. Lett. 50, 186 (1983)]. For strong Coulomb interaction among the suspended viruses no adequate theory is available. Therefore, the data achieved under these conditions are interpreted in terms of the corresponding results of the non-Coulomb interacting samples.