  We prove convergence of suitable subsequences of weak solutions of a diffuse
interface model for the two-phase flow of incompressible fluids with different
densities with a nonlocal Cahn-Hilliard equation to weak solutions of the
corresponding system with a standard "local" Cahn-Hilliard equation. The
analysis is done in the case of a sufficiently smooth bounded domain with
no-slip boundary condition for the velocity and Neumann boundary conditions for
the Cahn-Hilliard equation. The proof is based on the corresponding result in
the case of a single Cahn-Hilliard equation and compactness arguments used in
the proof of existence of weak solutions for the diffuse interface model.
