Gross features of linearly viscoelastic flow are related to corresponding features of Newtonian viscous flow. A step change in pressure gradient produces particle displacements that are asymptotic (fort→∞) to those in a Newtonian flow startingTunits of time earlier.Tis the mean relaxation time of the fluid. A step change in flux requires a pressure loss that is asymptotic to the loss in a Newtonian flow startingTunits of time later. Results are independent of cross‐sectional shape, but require flow slow enough that terms of third order in shear per relaxation time are negligible.