  In the classical Lagrangian approach to conservation laws of gauge-natural
field theories a suitable (vector) density is known to generate the so--called
{\em conserved Noether currents}. It turns out that along any section of the
relevant gauge--natural bundle this density is the divergence of a
skew--symmetric (tensor) density, which is called a {\em superpotential} for
the conserved currents.
  We describe gauge--natural superpotentials in the framework of finite order
variational sequences according to Krupka. We refer to previous results of ours
on {\em variational Lie derivatives} concerning abstract versions of Noether's
theorems, which are here interpreted in terms of ``horizontal'' and
``vertical'' conserved currents. The gauge--natural lift of principal
automorphisms implies suitable linearity properties of the Lie derivative
operator. Thus abstract results due to Kol\'a\v{r}, concerning the integration
by parts procedure, can be applied to prove the {\em existence} and {\em
globality} of superpotentials in a very general setting.
