Double-helix DNA molecules can be found under different conformational structures driven by ionic and hydration surroundings. Usually, only the B-form of DNA, which is the only form stable in aqueous solution, can be studied by dielectric measurements. Here, the dielectric responses of DNA molecules in the A- and B-form, oriented co-linearly within fibres assembled in a film have been analyzed. The dielectric dispersion, permittivity and dissipation factor, have been measured as a function of frequency, strength voltage, time, temperature and nature of the counter-ions. Besides a high electrode polarization component, two relaxation peaks have been observed and fitted by two Cole-Cole relaxation terms. In the frequency range that we investigated (0.1 Hz to 5 ·10(6) Hz) the dielectric properties are dominated by the mobility and diffusivity of the counter-ions and their interactions with the DNA molecules, which can therefore be characterized for the A- and B-forms of DNA.