  We present a new family of spherically symmetric models for the luminous
components of elliptical and spiral galaxies and their dark matter haloes. Our
starting point is a general expression for the logarithmic slope $\alpha(r) =
d\log{\rho}/d\log{r}$ from which most of the cuspy models yet available in
literature may be derived. We then dedicate our attention to a particular set
of models whose logarithmic slope is a power law function of the radius $r$
investigating in detail their dynamics assuming isotropy in the velocity space.
While the basic properties (such as the density profile and the gravitational
potential) may be expressed analytically, both the distribution function and
the observable quantities (surface brightness and line of sight velocity
dispersion) have to be evaluated numerically. We also consider the extension to
anisotropic models trying two different parameterization. Since the model
recently proposed by Navarro et al. (2004) as the best fit to their sample of
numerically simulated haloes belongs to the family we present here, analytical
approximations are given for the most useful quantities.
