The evolution of coherent structures in a 2-D time-developing mixing layer of the Oldroyd-B fluids are examined numerically. The results indicate that adding polymer to the Newtonian fluids will cause stronger vorticity diffusion

accompanied with weaker fundamental and subharmonical perturbations

less intense vortex roll-up and pairing and slower rotational motion of pairing vortices. When Weissenberg number is up to 10

the vorticity gradients are enhanced and even the vorticity with opposite sign to the mean vorticity appears at the region where there is a build - up of polymer first normal stress difference. The vorticity with opposite sign results in the absence of the usual quasi - steady state of the primary vortex

and disappears due to the collapse of polymer normal stress difference if there exist pairing modes. The time when the consecutive rollers are completely coalesced into one is delayed in the viscoelatic mixing layer compared to the Newtonian one of the same total viscosity.