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The numerical simulations of negative corona discharge in Trichel pulse mode are carried out with the calculation of evolution of azimuthal perturbations. It is found the azimuthal instability with increment corresponding to avalanche development. This instability is suppressed at the nonlinear stage and does not lead to the process branching. The result is also applicable to the azimuthal instability of the cathode directed streamer, found earlier. The difference in their increments is followed from the difference in courses of the processess, which is discuss.

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The numerical simulations of the cathode directed streamer propagation in the discharge gap, with the streamer going out to cathode, are carried out. The processes are found, which take place near anode and contribute to the formation of the first of two maxima of total current time dependence. The factors are considered, which determine the propagation of the ionization process at the final stage, when the streamer approaches the cathode, and the ionization wave is propagating along the cathode surface.