  We present a model to describe the nonlinear response to a direct dc current
applied to a two-dimensional electron system in a strong magnetic field. The
model is based on the solution of the von Neumann equation incorporating the
exact dynamics of two-dimensional damped electrons in the presence of
arbitrarily strong magnetic and dc electric fields, while the effects of
randomly distributed impurities are perturbatively added. From the analysis of
the differential resistivity and the longitudinal voltage we observe the
formation of negative differential resistivity states (NDRS) that are the
precursors of the zero differential resistivity states (ZDRS). The theoretical
predictions correctly reproduce the main experimental features provided that
the inelastic scattering rate obey a $T^2$ temperature dependence, consistent
with electron-electron interaction effects.
