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The low-frequency dielectric response of the surface stabilized ferroelectric liquid crystal (SSFLC) cells has been investigated. It was found that the dielectric response depends on the type of the smectic layer structure present and the cell thickness. An analytical solution to the equation of motion that describes the dynamics of SSFLC cells in the presence of a weak external field for both bookshelf and chevron geometries has been developed. This result is used to calculate the dielectric response of these SSFLC cells. Experimental values of the dielectric relaxation strength and the relaxation frequency show good agreement with those predicted by the theoretical model for the chevron structure. An observed discrepancy between the theory and the experimental results for the bookshelf structure is discussed.