  The general, non-dissipative, two-fluid model in plasma physics is
Hamiltonian, but this property is sometimes lost or obscured in the process of
deriving simplified (or reduced) two-fluid or one-fluid models from the
two-fluid equations of motion. To ensure that the reduced models are
Hamiltonian, we start with the general two-fluid action functional, and make
all the approximations, changes of variables, and expansions directly within
the action context. The resulting equations are then mapped to the Eulerian
fluid variables using a novel nonlocal Lagrange-Euler map. Using this method,
we recover L\"{u}st's general two-fluid model, extended MHD, Hall MHD, and
electron MHD from a unified framework. The variational formulation allows us to
use Noether's theorem to derive conserved quantities for each symmetry of the
action.
