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We develop the new model for analyzing ultrashort terahertz pulse propagation in nonequilibrium nonstationary plasma channels [1]. The response of the plasma to the terahertz frequency band radiation is investigated on the basis of the kinetic Boltzmann equation for the temporal behavior of the electron velocity distribution function (EVDF) in an arbitrary external electric field and allows to take into account both temporal retardation of the EVDF evolution with respect to the external electric field and the effect of the relaxation of the strongly nonequilibrium EVDF due to elastic electron - atomic collisions in nonequilibrium and nonstationary plasma formed in gases by multiphoton ionization by UV laser radiation. The possibility of THz pulse amplification is analyzed in dependence on THz pulse and plasma parameters. Proposed model is highly suitable to be incorporated in the self-consistent analysis for short THz pulse propagation in a plasma channel based on joint solution of Boltzmann equation for EVDF in a plasma and wave equation beyond the paraxial approximation [2]. Further we are going to develop this approach for analysis of THz pulse propagation in plasma channels with higher electron density when electron-electron collisions are of importance and provide more rapid relaxation of energy spectrum in plasma. Rapid relaxation of the spectrum also take place in the air (or nitrogen) plasma where the effect of amplification of extremely short THz is also possible. REFERENCES: [1] A. V. Bogatskaya and A. M. Popov Laser Phys. Lett., vol.16, (2019) accepted for publication [2] A. V. Bogatskaya, E. A. Volkova and A. M. Popov Laser Phys., vol.29, (2019) submitted.