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Smectic elastomers [1] are rubbery materials that have the macroscopic symmetry properties of smectic liquid crystals [2]. They are sure to have intriguing properties, some of which have already been studied experimentally and/or theoretically [1]. Very recently, seminal progress has been made on smectic-C (SmC) elastomers forming spontaneously from a smectic-A (SmA) phase upon cooling. Hiraoka et al. [3] for the first time produced a monodomain sample of such a material and carried out experiments demonstrating its spontaneous and reversible deformation in a heating an cooling process. Also very recently, it was discovered theoretically that such a material exhibits the fascinating phenomenon of soft elasticity [4], i.e., certain elastic moduli vanish as a consequence of the spontaneous symmetry breaking wherefore strains along specific symmetry direction cost no elastic energy and thus cause no restoring forces. On one hand, due to the aforementioned experimental advances, dynamical experiments on soft SmC elastomers, such as rheology experiments of storage and loss moduli or Brillouin scattering measurements of sound velocities, seem within reach. On the other hand, there exists, to our knowledge, no dynamical theory that could be helpful in interpreting these kinds of experiments. Here we present a theory for the low-frequency, long-wavelength dynamics of soft SmC elastomers with locked-in layers that goes beyond pure hydrodynamics. As in standard elastic media and nematic elastomers [5] a purely hydrodynamical theory of SmC elastomers involves only a displacement field u and not the Frank director n, which relaxes to the local strain in a nonhydrodynamic time τn. We go beyond hydrodynamics, by including n in our theory, because dynamical experiments, like rheology measurements, typically probe a wide range of frequencies that extends from hydrodynamic regime to frequencies well above it. Smectic elastomers are, like any elastomers, permanently crosslinked amorphous solids whose static elasticity is most easily described in Lagrangian coordinates in which x labels a mass point in the undeformed (reference) material and R(x) = x + u(x), where u(x) is the displacement variable, labels the position of the mass point x in the deformed (target) material. Lagrangian elastic energies are formulated in terms of the strain tensor u which, in its linearized form, has the components uij = 1 2 (ηij + ηji), where ηij = ∂jui are the components of the displacement gradient tensor η. The elastic energy density f of the SmC elastomers of interest here can be divided into two parts [4]