Data on the solidus surface of the partial TiRh-Rh-AlRh system and results of metallography, x-ray diffraction, and differential thermal and electron microprobe analyses of its as-cast alloys are used to project the liquidus surface of this system onto the concentration triangle and examine the processes occurring in the crystallization of its alloys for the first time. This makes it possible to plot the melting diagram of the partial TiRh-Rh-AlRh system. Its liquidus surface is completed with four surfaces of primary crystallization of solid solutions based on rhodium and phases based on binary compounds formed in the bounding binary Al-Rh and Ti-Rh systems. In the partial TiRh-Rh-AlRh system, there are two invariant four-phase equilibria involving liquid; one of them is peritectic (at 1714°C) and the other is eutectic (at 1675°C). These four-phase equilibria also include five monovariant three-phase equilibria involving a liquid phase.