  The Hodge dual operator, recently introduced for supermanifolds, is used to
reformulate super Yang-Mills and supergravity in $D=4$. We first recall the
definition of the Hodge dual operator for flat and curved supermanifolds. Then
we show how to recover the usual super-Yang-Mills equations of motion for
$N=1,2$ supersymmetry, and the obstacles (as seen from Hodge dual point of
view) in the case $N \geq 3$. We reconsider several ingredients of
supergeometry, relevant for a superspace formulation of supergravity, in terms
of the Hodge dual operator. Finally we discuss how $D=4$ and $N=1$ supergravity
is obtained in this framework.
