The present work is a discussion on hydrogen solubility and diffusivity in the TiAl-L1(0) system using first-principles calculations. First, ground-state properties of the TiAl-L1(0) system are presented and discussed using elastic, phonon and thermal properties. They are compared with literature results. After having analyzed the geometry of L1(0) using the space-group theory, ten potential interstitial sites for hydrogen insertion were identified (among which the various octahedral and tetrahedral sites). After relaxation, only three configurations remained stable, but one site was significantly more stable than the others. The interactions between hydrogen and metal atoms are then described and analyzed by computing different quantities such as phonon properties, charge transfers, formation volumes and elastic dipoles. Diffusion mechanisms were then studied by analyzing the possible displacements at the atomic scale, and the diffusion coefficient of H atoms in TiAl was finally computed. Results how that H diffusion is strongly anisotropic. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.