The aim of this diploma thesis was the microstructural characterisation of TiAl alloy TNM-B1 in the cast as well as in the thermomechanically processed state. Main focus of interest was directed towards the development of a heat treatment resulting in optimized microstructures with well-balanced mechanical properties. It was shown how grain size and phase distributions can be controlled by employing optimized heat parameters. For characterisation of the different microstructures, a data analysis allowing quantitative analysis and thorough interpretation of images obtained both by scanning electron microscopy as well as light-optical microscopy on colour-etched specimens was developed. The entire production process, starting from centrifugal casting followed by hot forging and ending with multi-step heat treatments has been investigated and the effect on phase distribution and grain size variation was analysed. The occurring mechanism during formation of the microstructure are described and supported by plausible models.