  We generalize the fermion Chern-Simons theory for the Fractional Hall Effect
(FQHE) which we developed before, to the case of bilayer systems. We study the
complete dynamic response of these systems and predict the experimentally
accessible optical properties. In general, for the so called $(m, m, n)$
states, we find that the spectrum of collective excitations has a gap, and the
wave function has the Jastrow-Slater form, with the exponents determined by the
coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it
i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode
which may be related with the spontaneous appearance of the interlayer
coherence. Our results also indicate that the gapless mode makes a contribution
to the wave function of the $(m,m,m)$ states analogous to the phonon
contribution to the wave function of superfluid $\rm{He}_4$. We calculate the
Hall conductance, and the charge and statistics of the quasiparticles. We also
present an $SU(2)$ generalization of this theory relevant to spin unpolarized
or partially polarized single layers.
