On-line rheometers are widely used as sensors in the process industries, and the most common type is a capillary viscometer fed by means of a side stream and a gear pump. A limitation on the application of this type of instrument for process control is the signal delay associated with the time required for fluid to flow from the main flow line to the capillary and the flow in the capillary itself. An important aspect of the contribution of this flow time to the rheometer dynamics is Taylor diffusion, i.e. the axial spreading out of the flow front due to the nonuniform velocity profile. We show the effect of Taylor diffusion on the dynamic response of the shear stress at the wall of a tube for a power-law fluid.