The application of the asymptotic freedom hypothesis to consider the mechanics of deep inelastic scattering processes (DIS), allows one to reveal the elastic form of the parton (xama and xbmb) scattering also for hadron-hadron interactions of particles a and b having masses ma and mb with subsequent hadronization of them into the hadron showers. The elastic character of the parton scattering, in its turn, helps to define invariant variables analogoues to DIS (Bjorken xa, xb and square four-momentum transfer Q2) through the two-hadron showers in the c.m.s. of a and b particles.