The wave packet revivals constitute a central concept of X-ray spectroscopy with ultra-high spectral resolution. The revival phenomenon allows to resolve the anharmonical shift or rotational structure by means of time dependent measurements and makes X-ray pump-probe spectroscopy a powerful technique to study long-term dynamics of molecules in different phases. We study the revivals referring to the X-ray absorption spectrum of the NO molecule driven by strong infrared pulse. It is shown that the phase sensitive trajectories of the center of gravity of the wave packets and the X-ray spectra copy each other. (c) 2005 Elsevier B.V. All rights reserved.