In situ straining experiments in a high-voltage electron microscope have been performed on two-phase Ti-47at.%Al-2at.Cr-0.2at.%Si at room temperature and at 900 K. Two microstructures were investigated which were produced by thermomechanical treatments: a so-called near-gamma and a nearly lamellar microstructure. The processes controlling the motion of individual dislocations in the phase are very similar in both materials. At room temperature, ordinary dislocations and superdislocations show a jerky motion which is impeded by localized obstacles and jogs. At high temperature, the dislocations are smoothly bent or arranged in preferred orientations and move in a viscous way. This mode of motions as well as the nonplanar arrangement of dislocations point to the action of climb as an essential process during the high-temperature deformation of Ti-Al. These observations are very similar to those on Al-rich single phase TiAl investigated earlier. The considerably higher flow stress of the two-phase alloys is an effect of their particular microstructures, i.e. of grain boundaries and lamella interfaces.