  We study a very general four dimensional Field Theory model describing the
dynamics of a massless higher spin $N$ symmetric tensor field particle
interacting with a geometrical background.This model is invariant under the
action of an extended linear diffeomorphism. We investigate the consistency of
the equations of motion, and the highest spin degrees of freedom are extracted
by means of a set of covariant constraints. Moreover the the highest spin
equations of motions (and in general all the highest spin field 1-PI
irreducible Green functions) are invariant under a chain of transformations
induced by a set of $N-2$ Ward operators, while the auxiliary fields equations
of motion spoil this symmetry. The first steps to a quantum extension of the
model are discussed on the basis of the Algebraic Field Theory.Technical
aspects are reported in Appendices; in particular one of them is devoted to
illustrate the spin-$2$ case.
