A generalized approach, based on linear algebra, is described for processing exhaust gas analyser data. Systematic methods of deriving useful relationships from arbitrary data are proposed and used to produce several novel and useful results, as well as to show how existing relationships may be derived in forms that involve no approximations. The methods developed lend themselves to automatic real-time assessment of the consistency of gas analyser data, and in the case of inconsistencies, identifying plausible reasons. The approach is also used to develop methods to examine storage and release mechanisms within after-treatment devices, such as oxygen storage/release in three-way catalysts, soot oxidation in particle filters and water condensation/evaporation.