A formulation for parameter estimation in cubic equations of state (CEOS) models for phase equilibrium thermodynamics is proposed. This formulation guarantees for the regressed parameters that the predicted mole fractions correspond to stable equilibria, when standard methods fail and demonstrably entail erroneous process simulation results. The present formulation overcomes these deficiencies, which is predicated on a bilevel structure extending Mitsos et al. (2009a). That is, an upper-level (parameter fitting) problem is minimized, subject to multiple lower-level problems, which encode thermodynamic stability. The CEOS constitutes an equality constraint on the lower level, which adds to the difficulty of the bilevel program. For the VLE of C5H12/H2S, it is demonstrated that the method permits an acceptable fit with physically sensible CEOS root values. Thus, the regressed parameter values may be applied to, e.g., process simulation. (C) 2018 Elsevier Ltd. All rights reserved.