Abstract: In this paper,a statistical study is made of the evolution of X-ray radiation of 273 objects (235 quasars and 38 type I Seyferts) in the 0.5-4.5 keVband observed from the Einstein Observatory.On the L_x-z plot of these 273 objects,there seems to exist a natural physical sequence (the QE band),which connects the active galaxies such as quasars and Seyferts in the sense of energy and the mass distribution of the central compact objects (hence the distribution of accretion rates).On the basis of the spherically symmetric accretion model of a massive black hole,the preliminary analysis of this sequence shows that quasars may quickly cross the lower envelope of the QE band and leave it and then disappear.Due to large accretion rates,the time of staying on this QE band for high-redshift quasars is found to be comparatively short (～10⁶yr),while that for low-redshift quasars and type I Seyferts is longer (～10⁸yr).These results agree with observations.Therefore,active galactic nuclei such as quasars and Seyferts may be manifestations of galactic nuclei in an excited state under specific conditions.Using the available monochromatic radio,optical and X-ray luminosities l_r l_o and l_x of 107 quasars,we find that there exist two evolutionary stages in the optical luminosities of quasars: the optically bright and optically faint stages.In each of these stages,the parameters characterizing the typical properties of quasars are evidently distinctive.The change of spectrum types may imply that the radiation mechanisms in different energy regions are different.