The　mixed　effects　models　with　two　variance　components　are　often　used　to　analyze　longitudinal　data.　For　these　models,　we　compare　two　approaches　to　estimating　the　variance　components,　the　analysis　of　variance　approach　and　the　spectral　decomposition　approach.　We　establish　a　necessary　and　sufficient　condition　for　the　two　approaches　to　yield　identical　estimates,　and　some　sufficient　conditions　for　the　superiority　of　one　approach　over　the　other,　under　the　mean　squared　error　criterion.　Applications　of　the　methods　to　circular　models　and　longitudinal　data　are　discussed.　Furthermore,　simulation　results　indicate　that　better　estimates　of　variance　components　do　not　necessarily　imply　higher　power　of　the　tests　or　shorter　confidence　intervals.　(C)　2009　Elsevier　B.V.　All　rights　reserved.