In this paper a class of eigenvalue problems for hemivariational inequalities is studied which is defined on domains of the type (ω is a bounded open subset of , m1) and it involves concave–convex nonlinearities. Under suitable conditions on the nonlinearities, two nontrivial solutions are obtained which belong to a special closed convex cone of whenever the eigenvalues are of certain range. Our approach is variational, the main tool in our investigation is the critical point theory developed by Motreanu and Panagiotopoulos [Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Kluwer Academic Publishers, Dordrecht, 1999, Chapter 3].