Large-eddy simulations of stable and unstable ramjet operational modes are presented for an axisymmetric inlet-isolator-combustor configuration experimentally tested in the University of Illinois's ACT-II arc-heated combustion tunnel. A 32 species ethylene oxidation mechanism including nitrous oxide formation reactions is used in the calculations (HyChem FFCM 2.0). Conjugate heat-transfer models based on an assumed penetration depth of the applied heating load are used to account for localized wall heating during the short durations (∼0.2 to 0.3 s) of the parts of the experiments simulated in this work. The results show a marked sensitivity to trace levels of atomic oxygen (∼1% by mass) in the free stream, a consequence of the arc-heating process. Atomic oxygen significantly reduces ignition delay at the relatively low pressures present within the configuration. With 1% atomic oxygen in the free stream, a jet-wake stabilized, partially-premixed flame structure emerges during thermal-throat ramjet operation at an equivalence ratio of 1.24, in accord with available experimental pressure and imaging measurements. Considering the free stream as pure air results in a cavity-wake stabilized, rich premixed flame. Simulations of unstable ram-mode operation leading to inlet unstart at an equivalence ratio of 1.97 also indicate a sensitivity to the free-stream composition. A reduction in atomic oxygen concentration to 0.8% by mass yields good agreement with the experimentally-observed isolator shock-train propagation speed. Both the computational and experimental results indicate that the shock train accelerates before being disgorged from the inlet. This acceleration stems from a rapid increase in the sizes of regions of low speed, sometimes separated flow behind Mach disks that form as the shock train proceeds upstream.