[en] The behavior of hydrogen in perfect wurtzite beryllium oxide is herein investigated by means of electronic structure calculations based on density functional theory. The formation energies of the following set of states of hydrogen (H⁰, H⁺, H⁻, H₂, , ) are computed and their solubility is established as a function of temperature and pressure with emphasis given to conditions relevant for hydrogen-implanted materials. It is found that all magnetic states H⁰, , are unstable, while the relative stability of the non-magnetic states depends on the thermodynamic conditions: H₂ prevails above temperatures around 900 K at standard pressure, which is the lowest temperature in experiments measuring the diffusion coefficient of hydrogen in wurtzite beryllium oxide. Under hydrogen implantation, the total concentration of hydrogen is fixed by the implantation source; it is found that molecular hydrogen prevails starting from a very low total concentration in hydrogen (as low as 10⁻⁴⁰ at.fr.). Finally, the diffusion coefficient of H₂ in beryllium oxide is calculated and the results are compared with previous experimental data. (paper)