Heinz Hanßmann, Britta Sommer A degenerate bifurcation in the H\'enon-Heiles family (172K, PostScript, gzipped and uuencoded) ABSTRACT. The normalised H\'enon-Heiles family exhibits a degenerate bifurcation when passing through the separable case ``$\beta = 0$''. We clarify the relation between this degeneracy and the integrability at $\beta = 0$~. Furthermore we show that the degenerate bifurcation carries over to the H\'enon-Heiles family itself.