  We investigate the secular dynamics of a planetary system composed of the
parent star and two massive planets in mutually inclined orbits. The dynamics
are investigated in wide ranges of semi-major axes ratios (0.1-0.667), and
planetary masses ratios (0.25-2) as well as in the whole permitted ranges of
the energy and total angular momentum. The secular model is constructed by
semi-analytic averaging of the three-body system. We focus on equilibria of the
secular Hamiltonian (periodic solutions of the full system), and we analyze
their stability. We attempt to classify families of these solutions in terms of
the angular momentum integral. We identified new equilibria, yet unknown in the
literature. Our results are general and may be applied to a wide class of
three-body systems, including configurations with a star and brown dwarfs and
sub-stellar objects. We also describe some technical aspects of the
semi-numerical averaging. The HD 12661 planetary system is investigated as an
example configuration.
