Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls is extended to the flow of non-Newtonian viscoelastic fluids (known as Phan-Thein-Tanner (PTT)). Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficient Ki(t) is obtained exactly and numerically for linearized and exponential forms of the PTT fluids, respectively. The analysis leads to the novel result for K1 and K2(t) (which is a measure of the longitudinal dispersion coefficient of the solute). It is found that the value of K2(t) depends on the value of Deborah number (De=a measure of the level of elasticity in the fluid) whereas the value of K1 is constant in both cases. Finally, the effect of the Deborah number on the axial distribution of the mean concentration θm is investigated in detail. © 2002 Elsevier Science Ltd. All rights reserved.