  Two semi-analytical one-degree-of-freedom secular models are presented for
the motion of small bodies beyond Neptune. A special attention is given to
trajectories entirely exterior to the planetary orbits. The first one is the
well-known non-resonant model of Kozai (1962) adapted to the transneptunian
region. Contrary to previous papers, the dynamics is fully characterized with
respect to the fixed parameters. A maximum perihelion excursion possible of
16.4 AU is determined. The second model handles the occurrence of a mean-motion
resonance with one of the planets. In that case, the one-degree-of-freedom
integrable approximation is obtained by postulating the adiabatic invariance,
and is much more general and accurate than previous secular models found in the
literature. It brings out in a plain way the possibility of perihelion
oscillations with a very high amplitude. Such a model could thus be used in
future studies to deeper explore that kind of motion. For complex resonant
orbits (especially of type 1:k), a segmented secular description is necessary
since the trajectories are only "integrable by parts". The two models are
applied to the Solar System but the notations are kept general so that it could
be used for any quasi-circular and coplanar planetary system.
