For　a　general　linear　mixed　model　with　two　variance　components,　a　set　of　simple　conditions　is　obtained,　under　which,　(i)　the　least　squares　estimate　of　the　fixed　effects　and　the　analysis　of　variance　(ANOVA)　estimates　of　variance　components　are　proved　to　be　uniformly　minimum　variance　unbiased　estimates　simultaneously;　(ii)　the　exact　confidence　intervals　of　the　fixed　effects　and　uniformly　optimal　unbiased　tests　on　variance　components　are　given;　(iii)　the　exact　probability　expression　of　ANOVA　estimates　of　variance　components　taking　negative　value　is　obtained.