This study presents a dynamical systems model for long-term scenarios of demand in the aviation sector and resultant emissions of CO2 and NOx. We analyze the dynamics of demand growth for aviation, particularly in the emerging markets of developing nations. A model for subsonic aviation emissions is presented that reflects the consequences of industry forecasts for improvement in aviation fuel efficiency and emissions indices as well as projections of global economic and population growth over the next century. (Emissions of commercial supersonic aircraft are not modeled here.) The model incorporates a dynamical system of logistic growth towards a time-dependent capacity level. Using the long-term model, we present a set of projections of demand for aviation services, fossil fuel use, and emissions of carbon dioxide (CO2) and nitrogen oxides (NOx) through the year 2100; previous forecasts have not extended past 2040, We briefly discuss expectations for the distribution of NOx emissions over altitude and latitude.