Covariance and correlation structure analytic techniques can be used to test whether a specified correlation structure is an adequate model of the population correlation structure. These procedures include: (1) normal theory (NT) and asymptotically distribution free (ADF) covariance structure analysis techniques; and (2) NT and ADF correlation structure analysis techniques. This paper discusses Monte Carlo results on the Type I error control of correlation structure analytic techniques for tests of correlation pattern hypotheses under conditions of multivariate nonnormality. The results show the clear nonrobustness of normal theory correlation structure analysis procedures under conditions of nonnormality when testing the correlation pattern hypotheses such as the simplex or circumplex, but less so when testing the diagonal or block-diagonal correlation pattern hypotheses. This paper further demonstrates how improved Type I error control can be obtained by adopting asymptotically distribution free correlation structure analysis procedures. Three appendixes present population correlation matrices and model matrices, a discussion of distribution types, and a table of empirical Type I error rates. (Contains 6 tables, 8 figures, and 30 references.) (Author/SLD)