Abstract.  Ponderomotive acceleration of electrons by a short laser pulse undergoing relativistic self focusing in a plasma is investigated. The saturation in nonlinear plasma permittivity causes periodic self focusing of the laser. The periodicity lengths are different for different axial segments of the pulse. As a result pulse shape is distorted. An electron initially on the laser axis and at the front of the self focusing pulse gains energy from the pulse until it is run over by the pulse peak. By the time electron reaches to the tail, if pulse begins diverging, the deceleration of the electron is slower and the electron is left with net energy gain. The electrons slightly off the laser axis see a radial ponderomotive force too. Initially when they are accelerated by the pulse front the acceleration is strong as they are closer to axis. When they see the tail of the pulse (after being run by the pulse) they are farther from the axis and the retardation ponderomotive force is weaker. Thus there is net energy gain.