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Here we discuss the specific features of light-atom interaction at near-atomic laser field strength. The results of the computer simulations on the atomic silver interaction with the femtosecond pulses of Nd:YAG and Ti:Sapphire lasers are presented. We show how the photoelectron spectra are transformed when the laser field strength is varied from subatomic to near-atomic values. The probability of ionization as a function of the laser field strength demonstrates the effect of ionization stabilization [J.H. Hoogenraad, R.B. Vrijen, L.D. Noordam, Physics Letters A, 50(5), pp.4133 (1994)]. The origin of this effect is different in the region of subatomic and near-atomic fields. The mechanisms of ionization stabilization are discussed.