We present measurements and a theoretical concept of the nonlinear transport in the two-dimensional Wigner solid on the free surface of normal and superfluid 3He. We have observed the transition from Ohmic to nonlinear transport over a wide temperature range, from 200 microK to 200 mK at low electron velocities. The field-velocity (E-nu) characteristics show a nonmonotonic structure with a particular local maxima. We attribute this nonlinearity to the velocity-induced deformation of the periodic surface displacement due to the extremely strong damping in Fermi-liquid 3He. The calculated E-nu curves and thresholds are in good agreement with experiment.