Let $\Omega$ be a bounded domain in $\mathbb R^N$ and $m_1$, $m_2$ two functions in
$L^\infty(\Omega)$. In the present work, we study
a new spectrum constitued by the set of pairs $(\alpha,\beta)$ of $\R ^2$ for which the problem $$
\left\{
\begin{array}{rcr}
-\bigtriangleup u & = & \alpha m_1 u^+-\be m_2 u^- \quad\mbox{ in} \:\: \Omega,\\
u & = & 0 \quad \hspace{2,4cm}\quad\mbox{ on}\:\:
\partial\Omega,
\end{array}
\right. $$
has a nontrivial solution, where $u^\pm=\di\max(0,\pm u)$. We study then the nonresonance with
respect to this spectrum in a non autonomous problem.