On the basis of the proposed algorithm for calculation of the hadron reaction rates, the space-time structure of the relativistic nucleus-nucleus collisions is studied. The reaction zones and the reaction frequencies for various types of reactions are calculated for AGS and SPS energies within the microscopic transport model. The relation of the reaction zones to the kinetic and chemical freeze-out processes is discussed. It is shown that the space-time freeze-out layer is most extended in time in the central region, while, especially for higher collision energies, the layer becomes very narrow at the sides. The parametrization of freeze-out hypersurface in the form of specific hyperbola of constant proper time was confirmed. The specific characteristic time moments of the fireball evolution are introduced. It is found that the time of the division of a reaction zone into two separate parts does not depend on the collision energy. Calculations of the hadronic reaction frequency show that the evolution of nucleus-nucleus collision can be divided into two hadronic stages.