A new mathematical model of the local kinetic characteristic E = f ( i,τ ) of nickel oxide electrode NiOOН/Ni(OН)2 is presented. An object of the analysis is a flat crystal of an active substance of the ”h” thickness which models a particle in the limits of “2h” size. A mathematical model of the processes is based on the conception concerning the potential and polarization as the functions of protons concentration in the superficial layer of a crystal. Polarization shall be considered as a sum of concentrated, activated and ohmic components. A concept of coefficients of protons activity and proton vacancies of a crystal lattice is used. The electrode potential during discharge is determined by changing superficial concentration of protons. A diffusion coefficient, speed of protons electromigration and specific resistance of a solid phase are changed within a thickness of the crystal according to the change of protons concentration and coefficients of activity. Distribution of protons concentration is determined by numerical decision of one-dimensional sum of diffusional and electromigration transference.