  In the Peierls state very thin samples of TaS_3 (cross-section area \sim
10^{-3} mkm^2) are found to demonstrate smearing of the I-V curves near the
threshold field. With approaching the Peierls transition temperature, T_P, the
smearing evolves into smooth growth of conductance from zero voltage
interpreted by us as the contribution of fluctuations to the non--linear
conductance. We identify independently the fluctuation contribution to the
linear conductance near T_P. Both linear and non-linear contributions depend on
temperature with close activation energies \sim (2 - 4) x 10^3 K and apparently
reveal the same process. We reject creep of the {\it continuous} charge-density
waves (CDWs) as the origin of this effect and show that it is spontaneous phase
slippage that results in creep of the CDW. A model is proposed accounting for
both the linear and non-linear parts of the fluctuation conduction up to T_P.
