C. Landim, R. M. Sued, G. Valle Hydrodynamic limit of asymmetric exclusion processes under diffusive scaling in $d\ge 3$. (379K, Postscript) ABSTRACT. We consider the asymmetric exclusion process. We start from a profile which is constant along the drift direction and prove that the density profile, under a diffusive rescaling of time, converges to the solution of a parabolic equation.