Nonstationary kinetics, of the ion redistribution within the meniscus region during deposition of a charged Langmuir monolayer after beginning or stopping of the substrate motion is analyzed on the basis of the results of numerical simulations. The time evolution of the ions concentration profiles forming at the contact line and propagating toward the bulk solution is considered. It is shown that the diffusion front propagates much slower within the region of overlapping diffuse layers than outside of this region. At the beginning of the deposition process a region characterized by quasi-stationary behavior of the ion concentration and electric potential distributions is formed in close vicinity to the contact line. A stationary deposition regime is established when the region of quasi-stationary distributions reaches the external boundary of the Nernst layer provided that the substrate motion is not very fast, For the substrate velocities higher than the critical one the concentration near the contact line can decrease to such small values which do not allow a stable deposition process. The developed mathematical model allows addressing to transient regimes of the monolayer deposition which are very important for understanding the mechanisms leading to Meniscus instability.