Ignition of hydrogen and oxygen in counterflow was studied using asymptotic methods for temperatures above that of crossover. Starting with seven elementary reaction steps, a reduced mechanism was derived using chemical steady-state approximations for the O and OH radicals. An algebraic ignition criterion was derived using this mechanism which predicts the ignition state as a function of the parameters defining the system. This criterion successfully explains the behavior analogous to the "first" and "second" explosion limits observed in homogeneous hydrogen-oxygen mixtures. A bifurcation analysis was then performed to clarify the ignition behavior. This analysis demonstrated that an ignition turning point can occur solely through the interaction of radical species with no contribution from heat release. The source of this turning was found to be the reaction H + HO2 -> 2OH, confirming results from numerical calculations. Finally, the regimes in which abrupt or monotonic transition to an ignited state were recalculated including the effect of this reaction.