In the present work, the superplastic characteristics of some γ-TiAl alloys were analysed on the bases of experimental data reported in previous work, and their suitability for diffusion bonding was examined. The constitutive equation ∊ = A DGb/ kT ( b/ d)p ( σ− σ 0/ G)n can be used to describe superplasticity in γ-TiAl alloys, and the equation predicts n=2, p=2, and activity energy Q=220 kJ mol−1. It is suggested that the diffusion bonding model for γ-TiAl alloys should be considered two stages, i.e. a plastic deformation stage and a void shrinkage stage including both a diffusion controlled process and a plastic controlled process. Theoretical predictions for obtaining good bonding conditions were in good agreement with experimental results. Using a theoretical bonding model, a prediction map showing the relationship among temperature, applied stress and time for high quality diffusion bonding of superplastic γ-TiAl alloys was obtained.