  We describe a comprehensive model for systems locked in the Laplace
resonance. The framework is based on the simplest possible dynamical structure
provided by the Keplerian problem perturbed by the resonant coupling truncated
at second order in the eccentricities. The reduced Hamiltonian, constructed by
a transformation to resonant coordinates, is then submitted to a suitable
ordering of the terms and to the study of its equilibria. Henceforth, resonant
normal forms are computed. The main result is the identification of two
different classes of equilibria. In the first class, only one kind of stable
equilibrium is present: the paradigmatic case is that of the Galilean system.
In the second class, three kinds of stable equilibria are possible and at least
one of them is characterised by a high value of the forced eccentricity for the
`first planet': here the paradigmatic case is the exo-planetary system GJ-876,
  in which the combination of libration centers admits triple conjunctions
otherwise not possible in the Galilean case. The normal form obtained by
averaging with respect to the free eccentricity oscillations, describes the
libration of the Laplace argument for arbitrary amplitudes and allows us to
determine the libration width of the resonance. The agreement of the analytic
predictions with the numerical integration of the toy models is very good.
