Detailed chemical kinetics mechanisms are usually developed on the basis of spatially homogeneous calculations, but utilized in the simulation of very complex physical models. A fundamental question is if the importance of reactions is determined solely by the temperature and the actual concentration set or if it is also influenced by the thermal and diffusion couplings present in the physical model. A 46-step detailed mechanism of hydrogen oxidation was studied at equivalence ratios 0.5, 1.0, 2.0, and 4.0. Six physical models were designed (homogeneous explosion, burner-stabilized and freely propagating laminar flames, with and without thermal coupling), which provided very similar concentration curves as a function of temperature, while the local sensitivity functions revealed that the couplings in these models were very different. The importance of the reactions in every model was investigated by the principal component analysis of the rate sensitivity matrix F (PCAF method), exploiting that the results of this method depend only on the concentrations and temperature. A fundamentally different method, the principal component analysis of the local sensitivity matrix S (PCAS method) was used to extract information on the importance of reactions from the sensitivity functions. The PCAF and PCAS methods selected identical reduced mechanisms at all conditions, which shows that these are equally effective methods for determining a minimal reduced mechanism. The good agreement between the results of the two methods in the case of all models demonstrated that the importance of reactions was independent of the physical model into which the mechanism had been embedded. Thermal coupling did not have any effect on the selection of the reduced mechanisms. The difference between the importance of reactions in explosions and flames was caused by the difference of the concentrations in the low-temperature regions and not by the presence of diffusion. The reduced mechanisms contained 15 to 28 reaction steps, depending on the equivalence ratio and the type of the model. All species were retained in models of the combustion of lean and stoichiometric mixtures, while species H₂O₂ could be eliminated at rich conditions. Description of near stoichiometric conditions required more reaction steps, while rich combustion could be described by few reactions. An overall reduced mechanism, applicable in a wide range of conditions, contained 31 reaction steps. Results of the PCAS method revealed the global similarity relations of the sensitivity matrices of adiabatic explosions.