  We systematically study the question of identification and consistent
inclusion of the radion, within the Lagrangian approach, in a two brane
Randall-Sundrum model. Exploiting the symmetry properties of the theory, we
show how the radion can be identified unambiguously and give the action to all
orders in the radion field and the metric. Using the background field method,
we expand the theory to quadratic orders in the fields. We show that the most
general classical solutions, for the induced metric on the branes in the case
of a constant radion and a factorizable 4D metric, correspond to Einstein
spaces. We discuss extensively the diagonalization of the quadratic action.
Furthermore, we obtain the 4-dimensional effective theory from this and study
the question of the spectrum as well as the couplings in these theories.
