  We provide a complete classification of all abelian gauge invariant $p$-form
theories with equations of motion depending only on the second derivative of
the field---the $p$-form analogues of the Galileon scalar field theory. We
construct explicitly the nontrivial actions that exist for spacetime dimension
$D\leq11$, but our methods are general enough and can be extended to arbitrary
$D$. We uncover in particular a new $4$-form Galileon cubic theory in $D\geq8$
dimensions. As a by-product we give a simple proof of the fact that the
equations of motion depend on the $p$-form gauge fields only through their
field strengths, and show this explicitly for the recently discovered $3$-form
Galileon quartic theory.
