  Given a del Pezzo surface of degree d between 1 and 6, possibly with rational
double points, we construct a "tautological" holomorphic G-bundle over X, where
G is a reductive group which is an appropriate conformal form of the simply
connected complex linear group whose coroot lattice is isomorphic to the
primitive cohomology of the minimal resolution of X. For example, in case d=3
and X is a smooth cubic surface, the rank 27 vector bundle over X associated to
the G-bundle constructed above and the standard 27-dimensional representation
of E_6 is a direct sum of the line bundles associated to the 27 lines on X. We
also discuss the restriction of the G-bundle to smooth hyperplane sections.
