  After considering the kinetical interaction principle (KIP) introduced in
ref. Physica A {\bf296}, 405 (2001), we study in the Boltzmann picture, the
evolution equation and the H-theorem for non extensive systems. The
$q$-kinetics and the $\kappa$-kinetics are studied in detail starting from the
most general non linear Boltzmann equation compatible with the KIP.
