  We study general metric-affine theories of gravity in which the metric and
connection are the two independent fundamental variables. In this framework, we
use Lagrange-Noether methods to derive the identities and the conservation laws
that correspond to the invariance of the action under general coordinate
transformations. The results obtained are applied to generalized models with
nonminimal coupling of matter and gravity, with a coupling function that
depends arbitrarily on the covariant gravitational field variables.
