In near-rich limit hydrogen/air flames, for which the Lewis number is greater than unity and the Zeldovich number is large, pulsating modes of propagation were observed in a recent study through computational simulation with detailed chemistry and transport descriptions, with and without radiative heat loss. The study further showed that the stability boundary is minimally affected by radiative heat loss, while the concentration limit at which the pulsating flame extinguishes due to radiative heat loss is reduced from that of the steady-state limit. The present study extends this previous investigation to include the effect of elevated ambient pressure, for pressures ranging from 1 to 20 atmospheres, with emphasis on the influence of chain mechanisms in H-2/O-2 oxidation. Results showed that the critical equivalence ratio separating steady from pulsating propagation decreases monotonically with increasing pressure throughout this pressure range, that this onset of instability corresponds to the transition from the state dominated by H-O-2 branching to that of H-O-2 termination, and that a second stable regime was observed at high pressures and equivalence ratios where the weak HO2 chain-branching pathway is dominant. Furthermore, the extinction limits as determined for both the steady and unsteady propagation exhibit nonmonotonic behavior: decreasing with increasing pressure from I to 5 atm, and then increasing from 5 to 20 atm. This translates to a broader flammable range with increasing pressure for pressures in the range of 5 to 20 atm. (C) 2001 by The Combustion Institute.