The aim of this study was to investigate the structure, precipitation and dissolution behaviour of the hexagonal Ti2AlC phase, the so called H-carbides, in an advanced TNM alloy with the chemical composition of Ti-43.5Al-4Nb-1.5Mo-0.5C (all elements in at.%). Titanaluminides compete against conventional highly heat-resistant materials, such as Ni base superalloys or steels, which are commonly used in turbine blades of aircraft engines and as supercharger wheels in combustion engines. The main advantages are a low density, best high-temperature strength, excellent oxidation resistance and no tendencies for “titanium fire”. The investigated material is counted among the group of TNM alloys containing besides titanium and aluminium, also niobium and molybdenum. The main ordered intermetallic phases at room temperature are the γ-phase with a L10 structure, the α2-phase with a hexagonal D019 structure and the cubic βo-Phase with an ordered B2 structure. To increase the working temperature a gain of strength and creep resistance is required, which is reached by carbon addition. Even small amounts of carbon contribute to solid solution and precipitation hardening. By exceeding the solubility limit different carbide phases are precipitated. The determination and investigation of them was the main subject of this study. Transformation temperatures of present phases were determined by using dynamic differential scanning calorimetry measurements and afterwards were verified by selected heat treatment surveys. Targeted in-situ investigations within a high temperature laser scanning confocal microscopy were correlated with electron backscatter diffraction measurement to illustrate the orientation relationship between carbides and the present matrix. So basic knowledge about the formation and behaviour of H-carbides in the investigated TNM alloy was gained and an extended understanding of this alloys was built up.