The problem of classification is an old one that has application in biomedical, environmental, geophysical, medical, signal processing and in many other fields. There are numerous approaches to this problem using the statistical properties of the populations from which observations are drawn. In applications such as geophysical and signals processing there is a natural structure on the variance-covariance matrix of the observation vectors. The efficacy of classification is generally increased by taking that structure into account. One such structure that is used to model that variance-covariance matrix is the autoregressive circulant (ARC) structure. Classification rules have been developed for data that have an ARC covariance structure. The effectiveness of these rules has been shown by simulating data sets that have such ARC structure and comparing the error rates by using the rule that assumes an ARC structure, a compound symmetric (CS) structure and no structure. The results of these simulations show that the rule based on the correct structure has the lowest error rate and the rule based on the simple CS structure, in some cases, has a higher error rate than the rule based on no structure assumption.