Anisotropy of the electrical polarizability Deltaalpha of model DNA fragments in salt-free aqueous solutions is determined by Monte Carlo simulation. According to the fluctuation-dissipation theorem, the electrical polarizability of polyelectrolytes is related to the fluctuations of the dipole moment generated in the counterion atmosphere around the polyion in the absence of an applied electric field. At every simulation step we numerically sort counterions in increasing order of the sum of their distances from both ends of the polyion. Two kinds of counterions are recognized in distinct spatial distributions, allowing us to give a definition of condensed counterions for charged oligomers based on the simulation. The fraction of condensed counterions so determined approaches Manning's theoretical value as the molecular weight of polyelectrolytes increases. We calculate the contribution to the dipole moment from the first n counterions in the sorting list and define a partial polarizability tensor due to these n counterions. Its introduction enables us to distinguish between contributions to the polarizability from the two kinds of ions. Contribution from condensed counterions to the radial components of the polarizability tensor is very small as has hitherto often been postulated in various theories. However, contribution from the diffuse ion atmosphere is very large and cannot be neglected in the calculation of the anisotropy. Although in our simulations solvent convection is suppressed, characteristic features of the. electric properties of polyelectrolytes in aqueous solutions with no added salt are reproduced. The anisotropy of the electrical polarizability Deltaalpha of DNA in salt-free aqueous solution increases on dilution of the polymer concentration and is proportional to the second or higher power of the molecular weight. The similar to1 nm thick apparently stable ionic sheath in the immediate vicinity of the polyion should be distinguished from condensed counterions. It is the latter that behaves as a physical entity having characteristic electrical properties.