Abstract: In this paper, we consider the variance components model \left\\beginarraylE(\undersetn \times 1Y)=\undersetn \times 1\beta \\ D(Y)=\sigma_1^2 V_1+\sigma_2^2 V_2\endarray\right. and the admissibility of estimators for function g(β) is discussed. In §2, a necessary and sufficient condition that an estimator of p’β is admissible in the linear estimators class under the square loss is given. In §3, a necessary condition and a sufficient condition that an estimator of β is admissible in the linear estimators class under the square sum loss are given.