Anodic aluminum oxide has unique and highly attractive properties, including self-ordering of porous structure during anodization. Although anodization regimes leading to formation of highly ordered porous structures had been found experimentally, many aspects of the self-organization mechanism remain unsolved. Here, the detailed in situ small-angle X-ray diffraction study of the self-ordering in porous alumina films is reported. Structure evolution kinetics was deduced by a quantitative analysis of diffraction patterns combined with electron microscopy. The rate of pore ordering is shown to have maximal value at the initial anodization stage and rapidly decreases inversely proportional to t^0.2. Self-organization is shown to occur via growth of domains possessing preferential in-plane orientation and "death" of other domains, similar to Ostwald ripening governed by difference in pore growth rates for domains of different orientations. The process is accompanied by pore death and splitting making a significant impact on anodic oxides utilization in any mass-transport issues. This finding opens a novel approach for growth of highly ordered porous anodic oxide films.