  We study the low-frequency, long-wavelength dynamics of liquid crystal
elastomers, crosslinked in the smectic-$A$ phase, in their smectic-$A$, biaxial
smectic and smectic-$C$ phases. Two different yet related formulations are
employed. One formulation describes the pure hydrodynamics and does not
explicitly involve the Frank director, which relaxes to its local equilibrium
value in a non-hydrodynamic time. The other formulation explicitly treats the
director and applies beyond the hydrodynamic limit. We compare the
low-frequency, long-wavelength dynamics of smectic-$A$ elastomers to that of
nematics and show that the two are closely related. For the biaxial smectic and
the smectic-$C$ phases, we calculate sound velocities and the mode structure in
certain symmetry directions. For the smectic-$C$ elastomers, in addition, we
discuss in some detail their possible behavior in rheology experiments.
