  The statistical methods based on the classical Boltzmann-Gibbs (BG) approach
are at heart of essentially all descriptions of multiparticle production
processes. In many cases, however, one observes some deviations from the
expected behaviour. It is also known that conditions necessary for the BG
statistics to apply are usually satisfied only approximately. Two attitudes are
possible in such situations: either to abandon statistical approach trying some
other model or to generalise it to the so called nonextensive statistics
(widely used in the similar circumstances in many other branches of physics).
We shall provide here an overview of possible imprints of non-extensitivity
existing both in high energy cosmic ray physics and in multiparticle production
processes in hadronic collisions, in particular in heavy ion collisions.
