The isotopic composition of molecular hydrogen (H<sub>2</sub>) contains independent information for constraining the global H<sub>2</sub> budget. To explore this, we have implemented hydrogen sources and sinks, including their stable isotopic composition and isotope fractionation constants, into the global chemistry transport model TM5. For the first time, a global model now includes a simplified but explicit isotope reaction scheme for the photochemical production of H<sub>2</sub>. We present a comparison of modelled results for the H<sub>2</sub> mixing ratio and isotope composition with available measurements on seasonal to inter annual time scales for the years 2001–2007. The base model results agree well with observations for H<sub>2</sub> mixing ratios. For δD[H<sub>2</sub>], modelled values are slightly lower than measurements. A detailed sensitivity study is performed to identify the most important parameters for modelling the isotopic composition of H<sub>2</sub>. The results show that on the global scale, the discrepancy between model and measurements can be closed by adjusting the default values of the isotope effects in deposition, photochemistry and the stratosphere-troposphere exchange within the known range of uncertainty. However, the available isotope data do not provide sufficient information to uniquely constrain the global isotope budget. Therefore, additional studies focussing on the isotopic composition near the tropopause and on the isotope effects in the photochemistry and deposition are recommended.