A chemistry-climate model has been applied to study the radiative forcings generated by aircraft NOx emissions through changes in ozone and methane. Four numerical experiments, where an extra pulse of aircraft NOx was emitted into the model atmosphere for a single month (January, April, July, or October), were compared to a control experiment, allowing the aircraft impact to be isolated. The extra NOx produces a short-lived (few months) pulse of ozone that generates a positive radiative forcing. However, the NOx and O3 both generate OH, which leads to a reduction in CH4. A detailed analysis of the OH budget reveals the spatial structure and chemical reactions responsible for the generation of the OH perturbation. Methane's long lifetime means that the CH4 anomaly decays slowly (perturbation lifetime of 11.1 years). The negative CH4 anomaly also has an associated negative O3 anomaly, and both of these introduce a negative radiative forcing. There are important seasonal differences in the response of O3 and CH4 to aircraft NOx, related to the annual cycle in photochemistry; the O3 radiative forcing calculations also have a seasonal dependence. The long-term globally integrated annual mean net forcing calculated here is approximately zero, although earlier work suggests a small net positive forcing. The model design (e.g., upper tropospheric chemistry, convection parameterization) and experimental setup (pulse magnitude and duration) may somewhat influence the results: further work with a range of models is required to confirm these results quantitatively.