Summary: ``In this article, we consider the double eigenvalue problem for a $\phi$-Laplacian differential system. We prove the existence of positive solutions under the $\phi$-super-linear condition by means of the Guo-Krasnosel'skii fixed point theorem and the topological degree. It is shown that there exists a continuous curve splitting $\Bbb R^2_+\backslash \{(0, 0)\}$ into disjoint subsets such that systems has at least two, at least one, or no positive solutions according to parameters in different subsets.''