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Plant breeders traditionally have estimated genotypic and phenotypic correlations between traits using the method of moments on the basis of a multivariate analysis of variance (MANOVA). Drawbacks of using the method of moments to estimate variance and covariance components include the possibility of obtaining estimates outside of parameter bounds, reduced estimation efficiency, and ignorance of the estimators' distributional properties when data are missing. An alternative approach that does not suffer these problems, but depends on the assumption of normally distributed random effects and large sample sizes, is restricted maximum likelihood (REML). This paper illustrates the use of Proc MIXED of the SAS system to implement REML estimation of genotypic and phenotypic correlations. Additionally, a method to obtain approximate parametric estimates of the sampling variances of the correlation …