The kinetics of formation of semi-clathrate hydrates of tetra n-butyl ammonium fluoride (TBAF) with hydrogen (H2) and carbon dioxide (CO2) were studied in order to elucidate their potential for H2 storage as well as for CO2 sequestration. The influence of pressure, TBAF concentration (1.8 mol% and 3.4 mol%) and formation method (T-cycle method and T-constant method) on the hydrate nucleation, hydrate growth and the amount of gas uptake were determined. The results showed that the kinetics of formation of H2–TBAF semi-hydrates is favored at high pressures and TBAF concentrations. The TBAF concentration did not display a large influence on the kinetics of formation of CO2–TBAF semi-hydrates and pressure only showed a major influence on the formation rate. Instead, the induction time and the amount of CO2 consumed were favored at low temperatures. Additionally, in situ Raman spectroscopy was used to confirm the gas uptake in the hydrate structure and to observe structural changes.