This study investigates experimentally and computationally the existence of mild oxidation regimes and multiple ignition and extinction states in a system of nonpremixed, counterflowing hydrogen against heated air. Spontaneous Raman spectroscopy measurements of the water concentration show that up to three stable stationary states can be achieved for identical boundary conditions. Computationally, up to five steady-state solutions can be found, although only three are likely to be stable. This multiplicity is the result of combined thermokinetic and transport effects on the behavior of critical ignition and extinction states. To understand these effects, the system response was simulated using detailed kinetics and transport properties, and S-curve sensitivity was employed to identify the dominant chemistry near the critical states and to simplify the kinetic mechanism. The response to changes in the fuel concentration and system pressure was investigated experimentally by measuring the air temperatures corresponding to ignition and extinction, for fuel concentrations in the range of 6-38% H-2 in N-2 by volume, and pressures between 0.3 and 8 atm, at a constant pressure-weighted strain rate of 300 s(-1). The experimental results were found to agree well with the computational results. The experimental triple-solution multiplicity disappears for fuel concentrations in excess of similar to 25% or below similar to 7% H-2 in N-2, and was only found in the pressure range between similar to 1.5 and 7 atm, at 9% H-2 in N-2 and a pressure-weighted strain rate of 300 s(-1). In addition, the response to changes in the strain rate was studied computationally, for strain rates between 10 and 40,000 s(-1) and for air boundary temperatures ranging between 950 and 1100 K. The same features of up to five steady-state multiplicities and up to two ignition and extinction states can be obtained by changing the flow strain rate. In the strain rate space, the computational quintuple-solution multiplicity extends from similar to 100-10,000 s(-1), at 9% H-2 in N-2 and 4 atm.