  In this paper we consider in a bounded domain $\Omega \subset \mathbb{R}^N$
with smooth boundary an eigenvalue problem for the negative $(p,q)$-Laplacian
with a Steklov type boundary condition, where $p\in (1,\infty)$, $q\in
(2,\infty)$ and $p\neq q$. A full description of the set of eigenvalues of this
problem is provided, thus essentially extending a recent result by Abreu and
Madeira [1] related to the $(p,2)$-Laplacian.
