The phase behaviour of dilute mixtures of He in near-critical fluid Hg has been studied within the ranges 69 MPa to 332.5 MPa, 1433 K to 1882 K and amount-of-substance fractions x(He) within the values 0.0018 and 0.1020. A high-pressure and high-temperature vessel was filled with known amounts of He and Hg (synthetic method) and heated; an isochoric record of p and T was made while the temperature was gently decreased and the transition from homogeneous to two-phase systems was indicated by abrupt slope changes in the p-against-T isochores. Two distinct fluid phases are shown to exist in (helium+mercury) at temperatures and pressures higher than those corresponding to the critical point of pure mercury ("fluid-fluid equilibrium of the first type") and the system’s critical line, beginning at the critical point of pure Hg, runs steeply to higher pressures and temperatures. Solubility values as high as 0.28 mol . dm(-3) were measured for He in near-critical fluid Hg, in contrast to the much lower values estimated for He dissolved in metallic liquid Hg at sub-critical temperatures. The isobaric solubility of He in Hg increases with temperature for super-critical pressures, so that (helium+mercury) shows a positive enthalpy and entropy of dissolution under these conditions. At sufficiently high density, non-metallic near-critical Hg experiences a transition to a metallic state, resulting in a strong repulsive interaction between dissolved He and the surrounding conduction electrons, and hence the isothermal solubility of He decreases.