It is a well established result of Stellar Dynamics that the density profile in the inner galactic regions plays a considerable role in constraining the amount of orbital anisotropy admissible in stellar systems. This book focuses on the unexplored effects of the density profile at large radii on the dynamical consistency, that is non-negativity of the distribution function associated to each density component in two-component galaxy models. The case in which the second component is a massive central black hole is also addressed. By constructing a family of models characterized by free internal and external density slopes, the role of the density profile in the external galactic regions is extensively investigated, and it is found that both externally and internally steeper density profiles offer the possibility to sustain more radial anisotropy. Remarkably, the very heart of this result is contained in a general yet simple necessary condition for model consistency, which is both interesting and useful for people who work on galaxy modelling.