Models are proposed which account for the brittleness of TiAl intermetallic. One of these models is based on the transformation of a glissile superdislocation into sessile non-planar configurations (1). The other is associated with the high Peierls stress that arises from directional bonds between Ti atoms. An adequate model should explain also the yield point temperature peak observed in TiAl. It has not yet been possible to choose an appropriate model on the basis of the experimental data available. To this end, detailed electron microscope studies of the dislocation structure of TiAl at different temperatures are required. It should be noted that in different alloys with superstructure L1o some model or other may be realized.