Abstract: In the modeling of cancer cell invasion of the extracellular matrix, a nonlocal reaction-diffusion-advection model was recently proposed to describe the interactions between cancer cells, extracellular matrix and matrix degrading enzymes. Under no-flux boundary conditions and some appropriate assumptions on initial data, it was shown that the model possesses an unique global classical solution which is uniformly bounded. Furthermore, under the additional assumptions and some other technical assumptions, it was proved that any classical solution of the model approaches the spatially uniform state as the time goes to infinity