A coupled chemistry radiation transport two-dimensional model of the lower and middle atmosphere was adapted to study the chemical composition of the atmosphere at preindustrial time and last glacial maximum (LGM). The model was constrained by trace gas concentrations (CO2, CH4, and N2O) inferred from polar ice core records. The formulation of tropospheric dynamics and chemistry was improved in order to more accurately simulate the transport and the oxidation processes below the tropopause. Our objectives are to infer the changes in middle-atmosphere temperature, ozone layer, and oxidation capacity of the atmosphere (e.g., methane lifetime) over the last 18,000 years. A middle-atmosphere cooling was obtained between LGM and preindustrial Holocene (PIH) as well as between PIH and present time. This is mainly due to changes in the CO2 and chlorofluorocarbon (CFC) concentrations, respectively. CFCs are also the main contributors to the middle-atmosphere ozone decrease since PIH. Between LGM and PIH the compensating effects of CO2 and N2O lead to little variation in stratospheric ozone. A 17% decrease in tropospheric OH was obtained between LGM and PIH, whereas the model provides a 6% OH increase since PIH. The corresponding changes in the methane sink are too small to have played a dominant role in the past methane concentration changes. Our model derived methane emissions for LGM, PIH, and present time are in good agreement with methane sources evaluated during these three periods.