INTRODUCTION This report describes the formulation and testing of a model for projecting certain statistics which are related to the ambient standard for photochemical oxidant. Specifically@ the model can be used to estimate how nearly the air quality of a region will comply with the National Ambient Air Quality Standard (NAAQS) for oxidant. We have cast the model in the form of a Markov chain with a finite number of states@ the states occurring at discrete time points. The chain is defined by a transition probability matrix with time-varying parameters. In the model formulation@ the probability of existence of a given state (air quality) ultimately depends on the primary pollutant emissions. The output of the model consists of the expected number of times a threshold oxidant concentration@ e.g.@ 0.08 ppm@ is exceeded in a specified time interval together with the long-run probability of exceeding the given threshold. Our outlook in formulating the Markovian model differs from the viewpoint which characterizes more common regression-type and deterministic models used in air pollution research. Briefly@ the difference between the Markovian and other models is that the latter's aim is to compute absolute concentrations@ whereas the Markovian model is concerned with finding the probability of occurrence of specified concentration levels. Thus@ rather than answering a question@ such as@ what is the highest oxidant concentration that can be expected@ the Markov-type model would provide the probability of exceeding a prescribed oxidant level. Clearly@ the statistical viewpoint is inherent in the Markovian approach. The use of this type of model must be tempered by observation of some caveats attendant to any statistical approach. Estimates will be clearly corrupted by either systematic or random errors in the measurements; especially if subsequent generations of instrumentation overcome these sources of inaccuracy. Moreover@ since mechanisms of causality are represented only indirectly at best@ the use of statistical models for conditions far from those from which they were derived may not give reliable estimates. This may be a source of problems@ for example@ if a model derived for concentrations far above the NAAQS must be applied to conditions designed to meet the NAAQS. Subject to the limitations stated above@ the statistical form of the NAAQS for oxidant makes the Markovian model especially pertinent for determining whether or not a region meets the standard. We shall now proceed to examine the NAAQS for photochemical oxidant and its relation to the Markov chain model