Let bea linear model with independently - not necessary normally – distribused error componentsϵjandwhereV(i=1, …p) are known diagonal matrices and theΘiare unknown scalars (veriance components). Starting from prior distributions with respect to β and Θ BAYES solutions for four elasses of quedratie unblased estimaters for linear functions of the vaciance components are given. They result from solutions of linear equation systems and is general they depend - beside on the experimental design (X,U,V1,…Vp) -– only on skewness and kurtosis of the ϵ,j's and on the first two moments of the prior distribution. For special models there oxist solutions depending neither on the prior distribution nor on the distribution of the ϵj's.