  We develop a kinetic theory for strongly correlated disordered
one-dimensional electron systems out of equilibrium, within the Luttinger
liquid model. In the absence of inhomogeneities, the model exhibits no
relaxation to equilibrium. We derive kinetic equations for electron and plasmon
distribution functions in the presence of impurities and calculate the
equilibration rate $\gamma_E$. Remarkably, for not too low temperature and bias
voltage, $\gamma_E$ is given by the elastic backscattering rate, independent of
the strength of electron-electron interaction, temperature, and bias.
