In　this　paper,　the　authors　address　the　problem　of　the　minimax　estimator　of　linear　combinations　of　stochastic　regression　coefficients　and　parameters　in　the　general　normal　linear　model　with　random　effects.　Under　a　quadratic　loss　function,　the　minimax　property　of　linear　estimators　is　investigated.　In　the　class　of　all　estimators,　the　minimax　estimator　of　estimable　functions,　which　is　unique　with　probability　1,　is　obtained　under　a　multivariate　normal　distribution.