We discuss theoretically the behavior of atomic Hydrogen under irradiation with strong light pulses in the soft X-ray spectral region. The method consists in the direct numerical solution of the time dependent Schrödinger equation. We find ranges of (high) peak incident intensity I0, where 2-photon absorption becomes more probable than 1-photon absorption. At very high intensity, the total ionization probability goes very close to 1 and then decreases as I0 is further increased.188201