We present experimental data and a theoretical analysis of nonequilibrium mobility of surface electrons in liquid helium. The experiments are carried out in the temperature range where electron mobility is limited by electron scattering at surface excitations of liquid helium (ripplons). Holding and driving electric fields of wide ranges are used in measurements. Special attention is paid to the condition of strong holding fields under which hot electrons are confined to the ground surface level. Depending on the relation between the momentum relaxation rate and electron-electron collision frequency, different theoretical approaches are used to describe the nonlinear mobility of surface electrons. The results obtained allow to estimate the range of physical parameters where experimental data can be described by the theory of nonlinear electron transport within the ground surface level.