  We study the quantum dynamics of superfluids of bosons hybridized with Cooper
pairs near Feshbach resonances and the influence of fermion-boson conversion on
Mott states. We derive a set of equations of motion which describe novel low
energy dynamics in superfluids and obtain a new distinct branch of {\em gapped}
collective modes in superfluids which involve anti-symmetric phase oscillations
in fermionic and bosonic channels. We also find that Mott states in general are
unstable with respect to fermion-boson conversion; particles become delocalized
and the off-diagonal long-range order of superfluids can be developed when a
finite conversion is present. We further point out a possible hidden order in
Mott states. It is shown that the quantum dynamics of Fermi-Bose states can be
characterized by either an effective coupled $U(1)\otimes U(1)$ quantum rotor
Hamiltonian in a large-N limit or a coupled XXZ $\otimes$ XXZ spin Hamiltonian
in a single-orbit limit.
