Dielectric properties of chiral smectic liquid crystals characterised by the occurrence of the C(α)(*) phase were investigated in the frequency range 10 Hz-1 MHz. In the range of existence of this phase the observed relaxation spectrum is composed of two kinds of mode, and not of a single one, as commonly thought. Phase modes of the Goldstone type coexist in it with an amplitude type soft mode. The share of the soft mode in the global value of electric permittivity ε can be dominant and attain 90%. A possible explanation for that effect is sought in the similarity to chiral phases of the de Vries type.