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A model is presented which allows us to analyze normal zone propagation in monolith conductors taking account of current diffusion, the conductor's nonlinear properties and current sharing. An analytical description of the current diffusion heat generation is given. It is used in a first order ordinary differential equation (ODE) to determine the normal zone longitudinal velocity Vnz and temperature profile. The method is illustrated on the examples of conductors with copper and aluminum stabilizers. It also allows us to account for the heat transferred into the insulation, which can notably reduce Vnz.