In many industrially important processes hydrogen chloride occurs as one of the major constituents. Due to its corrosive nature, hydrogen chloride is not an easy substance to handle in industrial or experimental facilities and, as a consequence, accurate basic data of its mixtures is scarce. In this study, we examine the ability of two theoretical approaches, PACT (perturbed anisotropic chain theory), and SAFT (statistical associating fluid theory), to predict the phase behaviour of three binary mixtures of hydrogen chloride with n-alkanes, In the PACT approach, the molecules are modelled with Lennard-Jones spherical segments with a contribution to describe the dipole of the hydrogen chloride molecule. The non-sphericity of the n-alkane molecules is accounted for via Prigogine's approximation for the external degrees of freedom. In the SAFT approach, the molecules are represented by chains of spherical repulsive segments with attractive short-range sites. Hydrogen chloride is represented by a single sphere, with two attractive sites to model the dipole of the molecule. Chain molecules, such as the n-alkanes, are modelled fusing together a number of spherical segments. No attractive sites are included as these molecules are non-polar. We treat the long-range dispersion forces via variable-range square-well potentials; with the SAFT-VR approach. We find that both approaches accurately reproduce the experimental phase behaviour of the three mixtures for wide ranges of temperature and pressure. In the case of the SAFT-VR approach, both the critical region and the low temperature region are well represented with one set of parameters. However, the PACT approach requires two different sets of parameters: one for the critical region and one for lower temperature regions.