  We investigate the time evolution of a model system of interacting particles,
moving in a $d$-dimensional torus. The microscopic dynamics are first order in
time with velocities set equal to the negative gradient of a potential energy
term $\Psi$ plus independent Brownian motions: $\Psi$ is the sum of pair
potentials, $V(r)+\gamma^d J(\gamma r)$, the second term has the form of a Kac
potential with inverse range $\gamma$. Using diffusive hydrodynamical scaling
(spatial scale $\gamma^{-1}$, temporal scale $\gamma^{-2}$) we obtain, in the
limit $\gamma\downarrow 0$, a diffusive type integro-differential equation
describing the time evolution of the macroscopic density profile.
