Shear-thinning viscosities have been investigated for dilute solutions (c < c*) of high-molecular weight polymers, namely, poly(ethylene oxide) (PEO) and polyacrilamide in water and polyisobutylene in kerosene. Measurements have been performed using capillary viscometers and a Zimm-Crothers viscometer with rotors having angular velocities of different magnitude. Shear rate was varied within the range of 0.1-3000 s-1. This made it possible to obtain full curves of viscosity versus shear rate. Owing to a high measurement accuracy, significant data were obtained using concentrations as low as 5 ppm. For the PEO solutions, the shear-rate dependence of viscosity was investigated as a function of concentration and temperature of the solution as well as molecular weight of the dissolved polymer. The data were compared with theoretical predictions based on the idea of molecular dispersion of the polymer in the solution at low concentrations. Experimental results were found to deviate significantly from the theory and this is explained by supermolecular organization characteristics of the high-polymer solutions even at low concentrations. A parameter was introduced : the relative amplitude of the shear-thinning viscosity. This parameter is important for describing hydrodynamic behavior of the polymer solutions.