  Some general theorems are established on the local BRST cohomology for not
necessarily Lagrangian gauge theories. Particular attention is given to the
BRST groups with direct physical interpretation. Among other things, the groups
of rigid symmetries and conservation laws are shown to be still connected,
though less tightly than in the Lagrangian theory. The connection is provided
by the elements of another local BRST cohomology group whose elements are
identified with Lagrange structures. This extends the cohomological formulation
of the Noether theorem beyond the scope of Lagrangian dynamics. We show that
each integrable Lagrange structure gives rise to a Lie bracket in the space of
conservation laws, which generalizes the Dickey bracket of conserved currents
known in Lagrangian field theory. We study the issues of existence and
uniqueness of the local BRST complex associated with a given set of field
equations endowed with a compatible Lagrange structure. Contrary to the usual
BV formalism, such a complex does not always exist for non-Lagrangian dynamics,
and when exists it is by no means unique. The ambiguity and obstructions are
controlled by certain cohomology classes, which are all explicitly identified.
