In this article, we consider a two-dimensional incompressible non-Newtonian model with memory. We prove the existence of uniform global attractors  where  is the scaling parameter in the memory kernel. Furthermore, we prove that the model converges to the classical two-dimensional non-Newtonian system in an appropriate sense as  In particular, we construct a family of exponential attractors  which is robust as

non-Newtonian, memory kernel, global attractor, exponential attractor.