Currently, the lattice-cluster theory (LCT) is the most convenient thermodynamic tool to describe the branching influence on the phase equilibrium of hyperbranched polymer systems. Unfortunately, until now all applications of the LCT to such systems were restricted to moderate pressure because of the assumption of a rigid lattice. However, there is also a compressible version of the LCT known since a long time. Here, unoccupied lattice sites (voids) are permitted to make the system compressible. Thus, a binary system A + B is treated as ternary system A + B + C where C represents the voids. In this paper, the very complex equations are essentially simplified resulting in an applicable notation. On this base a LCT equation of state is developed and applied to the calculation of the high pressure phase equilibria of carbon dioxide + Boltorn U3000 and of propane + Boltorn H3200. The polymers are fatty acid modified Boltorn H30 molecules (hyperbranched polyester of generation number g = 3). The calculated results agree reasonably well with the experimental data from literature. (C) 2013 Elsevier Ltd. All rights reserved.