Ignition in hydrogen–oxygen systems above crossover temperatures and under various conditions of pressure and composition is addressed computationally and by asymptotic methods. Different descriptions of the detailed chemistry are evaluated through comparison of computed and measured ignition times, and a balance between accuracy and simplicity is struck in selecting rate parameters to be used in investigating reduced chemistry. Through numerical calculations for isobaric, homogeneous, and adiabatic hydrogen–air mixtures it is shown that the detailed chemistry can be reduced to only six elementary steps for determining induction times over the range of conditions addressed. From these six steps, an analytical expression for ignition time is derived which agrees well with computational results concerning dependence on pressure, temperature, and composition. It is shown that O and OH maintain steady states during ignition for stoichiometric and fuel-rich mixtures, whereas H maintains, a steady state for sufficiently fuel-lean conditions. Simple asymptotic formulas for the induction times are derived for these two limits that demonstrate the limiting effect of O2 under rich conditions and of H2 under lean conditions. These formulas are combined in an approximate way to obtain an expression for the ignition time that can be used for all equivalence ratios.