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We analyze the first passage time problem for the electrochemical stochastic diffusion governed by the Fokker—Planck equation in the form of Cattaneo equation. We find the characteristic function of the first passage time for the stochastic process that we consider. We show that variance of the first passage time for the stochastic process that we consider coincides with variance of the first passage time for the process governed by Einstein stochastic equation. This means that the relaxation time involved into the Cattaneo equation does not influence a variance of first passage time for the stochastic process governed by the Cattaneo equation. The results mentioned above are of certain interest for a general theory of stochastic processes.