A 3D mesoscopic simulation of dislocation behaviour is adapted to the case of γ-TiAl. It shows that, in the temperature range of the stress anomaly, ordinary dislocation motion essentially proceeds through a series of pinning and unzipping processes on screw dislocations. Pinning points are cross-slip generated jogs, whose density increases with temperature. Unzipping of cusps restores the screw character of the dislocation. The balance between pinning and unzipping becomes increasingly difficult as temperature raises, and results in dislocation exhaustion. All these features agree with the so-called “Local Pinning Unzipping” mechanism.