  A systematic procedure is proposed for inclusion of Stueckelberg fields. The
procedure begins with the involutive closure when the original Lagrangian
equations are complemented by all the lower order consequences. The involutive
closure can be viewed as Lagrangian analogue of complementing constrained
Hamiltonian system with secondary constraints. The involutively closed form of
the field equations allows for explicitly covariant degree of freedom number
count, which is stable with respect to deformations. If the original Lagrangian
equations are not involutive, the involutive closure will be a non-Lagrangian
system. The Stueckelberg fields are assigned to all the consequences included
into the involutive closure of the Lagrangian system. The iterative procedure
is proposed for constructing the gauge invariant action functional involving
Stueckelberg fields such that Lagrangian equations are equivalent to the
involutive closure of the original theory. The generators of the Stueckelberg
gauge symmetry begin with the operators generating the closure of original
Lagrangian system. These operators are not assumed to be a generators of gauge
symmetry of any part of the original action, nor are they supposed to form an
on shell integrable distribution. With the most general closure generators, the
consistent Stueckelberg gauge invariant theory is iteratively constructed,
without obstructions at any stage. The Batalin-Vilkovisky form of inclusion the
Stueckelberg fields is worked out and existence theorem for the Stueckelberg
action is proven.
