Nonpremixed ignition of counterflowing H-2 against hot air is studied numerically with emphasis on developing simplifying approximations to the conservation equations governing this system. We derive and examine a number of different "skeletal" and "reduced" chemical reaction mechanisms that are used to simplify the full kinetic mechanism consisting of 9 species and 19 bidirectional elementary reaction steps. It is found that the use of inherently homogeneous approximations such as the steady-state or partial equilibrium approximations in the derivation of reduced reaction mechanisms can lead to significant errors in this inhomogeneous system. We demonstrate that reaction step R11 (H + HO2 --> 2OH) plays a critical step in kinetically controlled H-2-air ignition, and present a 6-step skeletal mechanism which represents the smallest set of elementary reactions that will provide proper turning point behavior in the first and second ignition limits. A new sensitivity analysis methodology is introduced that quantifies the sensitivity of the system response, particularly near the ignition turning point, to important parameters in the conservation equations. We also examine the so-called decoupled ignition environment approximation in which ignition takes place within a static ignition environment, consisting of the temperature and major species concentration profiles. that is decoupled from and can be solved independently of the minor species profiles.