  Weil algebra morphism induce natural transformations between Weil bundles. In
some well known cases, a natural transformation is endowed with a canonical
structure of affine bundle. We show that this structure arises only when the
Weil algebra morphism is surjective and its kernel has null square. Moreover,
in some cases, this structure of affine bundle is passed down to Jet spaces. We
give a characterization of this fact in algebraic terms. This algebraic
condition also determines an affine structure between the groups of
automorphisms of related Weil algebras
