In the in situ lamellar γ-TiAl based composites, very large elastic stresses (≈ 1GPa) would be generated at coherent interfaces between close packed planes for three reasons: the tetragonality of TiAl, the larger atomic spacing in α2-Ti3Al than in γ and the differences between thermal expansion coefficients in α2 and γ. These stresses appear to be partially relaxed by the creation of van der Merwe dislocations, diffusion across α2/γ interfaces and cracking along interfaces. Measurements of lattice parameters by Convergent Beam Electron Diffraction (CBED) reveal stresses of the order of 100MPa. The presence of these stresses and the very specific form of the resulting stress tensor are used to discuss the hard/soft mode deformation of TiAl composites.