The non-linear dynamics of electron excitation in diatomic molecules is studied for ultra-short laser pulse with lambda = 147 nm. r = I fs and peak intensities I = 10(13)-10(15) W/cm(2). The electromagnetic wave frequency is in resonance to an electronic transition in the molecule. The molecule is modeled by a system of two active I D electrons moving in the field of a frozen core, The time dependences of electron density distribution, electron energy, and one-electron/two-electron ionization probability are calculated and show the effect of giant above-threshold absorption in the pulse of intensity I similar to 10(16) W/cm(2). (C) 2002 Elsevier Science B.V. All rights reserved.