In this paper，1inear models with p variance components are considered and the explicit and easy computable expressions for Bayes invariant quadratic unbiased estimates (BAIQUE's) are presented. The class of BAI-QUE's is proved to form the entire class of admissible invariant quadratic unbiased estimates. A necessary and sufficient condition for the existence of admissible nonegative definte quadratic unbiased estimates is given.