Problems　of　the　simultaneous　optimal　estimates　and　the　optimal　tests　in　general　mixed　models　are　considered.　A　necessary　and　sufficient　condition　is　presented　for　the　least　squares　estimate　of　the　fixed　effects　and　the　analysis　of　variance　(Hendreson　III＇s)　estimate　of　variance　components　being　uniformly　minimum　variance　unbiased　estimates　simultaneously.　This　result　can　be　applied　to　the　problems　of　finding　uniformly　optimal　unbiased　tests　and　uniformly　most　accurate　unbiased　confidential　interval　on　parameters　of　interest,　and　for　finding　equivalences　of　several　common　estimates　of　variance　components.