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.
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