Accurate modelling of the global distribution of trace gases in the atmosphere is necessary to understand the sources and sinks (chemical , physical or biological) that control the global budgets of the radiatively and chemically important gases. This effort continues the basic studies in theoretical modeling of the global composition of the atmosphere. First an investigation of how to improve the manner in which the physical / chemical process in global 3-D models (e.g., chemistry, transport and diffusion) are coupled with the high-order numerical methods used in calculating the transport of tracers, will be undertaken. Second, the developments of current research on three-dimensional chemical transport models (CTM) for stratospheric ozone will be used to examine how stratosphere-troposphere exchange controls the abundances of O3 and NOy in the upper troposphere.