<p>Alloys of hafnium with refractory platinum-group metals (in particular, rhodium and iridium) are of interest as high-temperature creep-resistant structural materials. The scientific basis for the design of new structural alloys with a tailored and controllable combination of properties is provided by phase diagrams of the respective multicomponent systems and related information on physicochemical interactions (crystal structure of solid phases and thermodynamic properties of solid and liquid phases). Information on phase equilibria in the Hf–Rh–Ir system was unavailable at the beginning of our research. Based on experimental findings, the solidus and liquidus surfaces, melting diagram, and Scheil diagram were constructed for the first time. The complexity of the phase equilibria required more detailed understanding of alloy formation processes. Therefore, vertical sections of the phase diagram were presented to illustrate phase transformations during alloy crystallization. Sixteen alloy compositions were prepared from iodide-refined hafnium (99.98%), rhodium wire (99.97%), and iridium powder (99.97%) by electric-arc melting. The alloys were annealed at subsolidus temperatures (20–50°C below the solidus). In as-cast and annealed states, the alloys were studied by microstructural analysis, differential thermal analysis, electron probe microanalysis, X-ray diffraction, and the Pirani–Alterthum technique. The experimental results were used to construct, for the first time, vertical sections of the ternary Hf–Rh–Ir phase diagram along the Ir : Rh = 1 : 1 line at the 15 at.% Ir, 10 and 42.5 at.% Rh, and 30, 33, and 62.5 at.% Hf isopleths. These sections demonstrate characteristic features of the phase equilibria in the system, particularly the alloy crystallization ranges and the nature of phase transformations.</p>