Ni and Ti aluminides show a high potential for lightweight applications at elevated temperatures. The strength of TiAl can be increased, if directionally solidified structures are producable. Recent developments of superalloys show that the laser rapid prototyping can be used to generate directionally solidified parts. To generate directionally solidified TiAl parts, first the problem of crack formation has to be solved. The solution was developed by the use of Ti48Al2Cr alloy and an adjusted cooling of the sample. Second the process parameters have to be chosen in a way, that directional solidification occurs. For this a macroscopic process simulation including the modeling of the feedstock material and a microstructure simulation is build up. The correlation of experiments and simulation will lead to process guidelines for laser rapid prototyping of directionally solidified TiAl parts. Paper text in German.