The influence of drag-reducing polymers on the time-averaged velocity gradient $\overline{S_x}$ and on the two components of the fluctuating velocity gradient a t the wall, sx and sz, has been studied for turbulent flow in a 1 in. pipe. The time-averaged velocity gradient is related to the time-averaged wall stress by Newton's law of viscosity. The view is taken that a comparison of the turbulence structure with and without polymers should be made at the same $\overline{S_x} $. Therefore all turbulence measurements have been normalized with wall parameters. On this basis we find that the changes in the intensity of sx, and in the shape of the spectral density functions for sx and sz are not as striking as the decrease in pressure drop caused by the addition of a polymer. The root-mean-square value of sz shows a significant decrease with an increase in drag reduction but the most spectacular change in turbulence structure seems to be associated with the transverse correlation coefficient. We conclude that the increase in drag reduction is accompanied by an increase of the size of longitudinally oriented eddies in the viscous sublayer. One possible explanation for this increase in size is that the influence of the polymer additives is such as to increase the viscous resistance in the transverse direction more than in the direction of mean flow.