  We consider a diffuse interface model for an incompressible isothermal
mixture of two viscous Newtonian fluids with different densities in a bounded
domain in two or three space dimensions. The model is the nonlocal version of
the one recently derived by Abels, Garcke and Gr\"{u}n and consists in a
Navier-Stokes type system coupled with a convective nonlocal Cahn-Hilliard
equation. The density of the mixture depends on an order parameter. For this
nonlocal system we prove existence of global dissipative weak solutions for the
case of singular double-well potentials and non degenerate mobilities. To this
goal we devise an approach which is completely independent of the one employed
by Abels, Depner and Garcke to establish existence of weak solutions for the
local Abels et al. model.
