  The complex of "stable forms" on supermanifolds is studied. Stable forms on
$M$ are represented by certain Lagrangians of "copaths" (formal systems of
equations, which may or may not specify actual surfaces) on $M\times\mathbb
R^D$. Changes of $D$ give rise to stability isomorphisms. The Cartan--de Rham
complex made of stable forms extends both in positive and negative degree and
its positive half is isomorphic to the complex of forms defined as Lagrangians
of paths. Considering the negative half is necessary, in particular, for
homotopy invariance.
  We introduce analogs of exterior multiplication by covectors and of
contraction with vectors. We find (anti)commutation relations for them. An
analog of Cartan's homotopy identity is proved. Before stabilization it
contains some "stability operator" $\sigma$.
