  Considering galaxies as self - gravitating systems of many collisionless
particles allows to use methods of statistical mechanics inferring the
distribution function of these stellar systems. Actually, the long range nature
of the gravitational force contrasts with the underlying assumptions of
Boltzmann statistics where the interactions among particles are assumed to be
short ranged. A particular generalization of the classical Boltzmann formalism
is available within the nonextensive context of Tsallis q -statistics, subject
to non -additivity of the entropies of sub - systems. Assuming stationarity and
isotropy in the velocity space, it is possible solving the generalized
collsionless Boltzmann equation to derive the galaxy distribution function and
density profile. We present a particular set of nonextensive models and
investigate their dynamical and observable properties. As a test of the
viability of this generalized context, we fit the rotation curve of M33 showing
that the proposed approach leads to dark matter haloes in excellent agreement
with the observed data.
