In　this　paper,　the　estimation　of　variance　components　in　the　linear　mixed　model　with　two　random　effects　is　investigated.　The　class　of　combination　estimates　based　on　the　quadratic　invariant　statistics　and　consistent　nonnegative　estimates　are　obtained.　Furthermore,　it　is　shown　that　the　consistent　nonnegative　estimate　dominates　ANOVA　estimate　under　some　conditions.