  We explore field theories of a single p-form with equations of motions of
order strictly equal to two and gauge invariance. We give a general method for
the classification of such theories which are extensions to the p-forms of the
Galileon models for scalars. Our classification scheme allows to compute an
upper bound on the number of different such theories depending on p and on the
space-time dimension. We are also able to build a non trivial Galileon like
theory for a 3-form with gauge invariance and an action which is polynomial
into the derivatives of the form. This theory has gauge invariant field
equations but an action which is not, like a Chern-Simons theory. Hence the
recently discovered no-go theorem stating that there are no non trivial gauge
invariant vector Galileons (which we are also able here to confirm with our
method) does not extend to other odd p cases.
