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We study the long time behavior of the Hele-Shaw-Cahn-Hilliard system (HSCH) which models two phase incompressible Darcian flow in porous media with matched density but arbitrary viscosity contrast. We demonstrate that the ω-limit set of each trajectory is a single sta-tionary solution of the system via Lojasiewicz-Simon type technique. Moreover, a rate of convergence has been established. Eventual regu-larity of weak solution, as well as existence of global classical solutions if the initial data is close to an energy minimizer or the Péclet number is sufficiently small are also proved in 3D. Keywords: AMS Subject Classification