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We present spherical, non-rotating, isotropic models of early-type galaxieswith stellar and dark-matter components both described by deprojected Sersicdensity profiles, and prove that they represent physically admissible stablesystems. Using empirical correlations and recent results of N-body simulations,all the free parameters of the models are expressed as functions of one singlequantity: the total (B-band) luminosity of the stellar component.  We analyze how to perform discrete N-body realizations of Sersic models. Tothis end, an optimal smoothing length is derived, defined as the softeningparameter minimizing the error on the gravitational potential for thedeprojected Sersic model. It is shown to depend on the Sersic index $n$ and onthe number of particles of the N-body realization.  A software code allowing the computations of the relevant quantities of one-and two-component Sersic models is provided. Both the code and the results ofthe present work are primarily intended as tools to perform N-body simulationsof early-type galaxies, where the structural non-homology of these systems(i.e. the variation of the shape parameter along the galaxy sequence) might betaken into account.

Sersic galaxy with Sersic halo models of early-type galaxies: a tool for N-body simulations