The　mixed-effects　models　are　an　important　class　of　statistical　models　that　are　used　in　many　fields　of　applications.　For　these　models,　we　compare　two　estimators　of　the　variance　components,　the　analysis　of　variance　(ANOVA)　estimator　and　the　spectral　decomposition　(SD)　estimator.　Based　on　the　spectral　decomposition　of　covariance　matrix　[A　new　method　of　spectral　decomposition　of　covariance　matrix　in　mixed　effects　models　and　its　applications,　Sci.　China,　Ser.　A,　2005,　48:　1451-1464],　we　establish　two　sufficient　conditions　for　the　identity　of　ANOVA　estimator　and　SD　estimator,　and　present　some　corresponding　statistical　properties　of　ANOVA　estimator　and　SD　estimator.　Applications　of　the　methods　to　circular　models　and　mixed　analysis　of　variance　models　are　discussed.