A new model of dielectric response of disordered substances is proposed. According to thismodel, the dielectric response is determined by the Drude drift currents localized in minimaof the random electrostatic potential. The drift of a charge carrier with mobilityμ in local parabolicpotential φ(x) = φmin + kx2/2 under an external alternating field results in the Debye-type response with ‘relaxation frequency’ωr = μk. The use ofdistribution functions G(k) for values k of local potential wells of a disordered material allows us to describe quantitativelyboth the spectral domains of the ‘nearly constant loss’ and the cases ofthe giant contribution to a low-frequency dielectric constant. In disorderedsubstance the response depends mainly on the width but not the shape ofG(k).