  The geometry of graded principal bundles is discussed in the framework of
graded manifold theory of Kostant-Berezin-Leites. In particular, we prove that
a graded principal bundle is globally trivial if and only if it admits a global
graded section and, further, that the sheaf of vertical derivations on such a
bundle coincides with the graded distribution induced by the action of the
structure graded Lie group. This result leads to a natural definition of the
graded connection in terms of graded distributions; its relation with Lie
superalgebra-valued graded differential forms is also exhibited. Finally, we
define the curvature for the graded connection; we prove that the curvature
controls the involutivity of the horizontal graded distribution corresponding
to the graded connection.
