In the paper a new class of tests for variance components in two variance components model is presented. The tests are based on nonnegative admissible invariant quadratic estimators of variance components. A comparison of the tests with the known ones are given. Two-way classification models corresponding to block designs are considered separately. Examples of these models are given, for which the power functions of the tests are computed by using Imhof’s procedure, and compared with the attainable upper bound obtained by using the Neyman–Pearson Lemma.