Following our earlier experimental and theoretical studies of the elf-organization in the Ni(II)-SCN- electroreduction at the streaming mercury electrode we describe analogous phenomena for the azide complexes of nickel(II). The complex electrochemical mechanism of this process is a source of multistability, if the appropriate serial ohmic resistance is present in the electric circuit. In dependence of the solution composition, bistability and tristability in the response of the electric current vs the applied voltage was observed. No spontaneous oscillations were reported for the studied process. The I-E characteristics of the Ni(II)-N-3(-) electroreduction, which exhibits the region of the negative differential resistance (NDR), are the source for the bistable behavior. If the composition of the sample is adjusted so that the current of the Ni(II) electroreduction in the NDR region overlaps significantly with the extra current, originating presumably from the catalytic reduction of azide ions, the second NDR region is also formed, and these complex characteristics are a source of the tristable behavior. The theoretical description of the observed multistable phenomena was made in terms of both the theory of electrode processes at a streaming electrode and standard techniques of nonlinear dynamics. The linear stability analysis led to theoretical bifurcation diagrams similar to the experimental ones. The reported tristability seems to be, one of the first experimental examples of such a behavior in electrochemical systems and one of only a few of its manifestations in chemical systems in general.