Summary. The general multivariate regression model with covariance components (the so called growth curve model) is studied in the paper. It is of the form Y = XBZ + [d], E[d] = 0, var(vec [d]) = W ® [d] =[d] We consider a parametric function [d]=[d]. There are derived conditions for unbiased and invariant estimation of parametric functions of the unknown parameters [d] and explicit formulas for locally best estimators under normality. The uniformly best estimator of the matrix W is also derived