  We study the effect of a strong electric field on the fluctuation
conductivity within the time-dependent Ginzburg-Landau theory for the case of
arbitrary dimension. Our results are based on the analytical derivation of the
velocity distribution law for the fluctuation Cooper pairs, from the Boltzmann
equation. Special attention is drawn to the case of small nonlinearity of
conductivity, which can be investigated experimentally. We obtain a general
relation between the nonlinear conductivity and the temperature derivative of
the linear Aslamazov-Larkin conductivity, applicable to any superconductor. For
the important case of layered superconductors we derive an analogous relation
between the small nonlinear correction for the conductivity and the
fluctuational magnetoconductivity. On the basis of these relations we provide
new experimental methods for determining both the lifetime constant of
metastable Cooper pairs above T_c and the coherence length. A systematic
investigation of the 3rd harmonic of the electric field generated by a harmonic
current can serve as an alternative method for the examination of the
metastable Cooper-pair relaxation time.
