  We prove existence of weak solutions for a diffuse interface model for the
flow of two viscous incompressible Newtonian fluids in a bounded domain by
allowing for a degenerate mobility. The model has been developed by Abels,
Garcke and Gr\"un for fluids with different densities and leads to a solenoidal
velocity field. It is given by a non-homogeneous Navier-Stokes system with a
modified convective term coupled to a Cahn-Hilliard system, such that an energy
estimate is fulfilled which follows from the fact that the model is
thermodynamically consistent.
