  Aims. Numerous trans-Neptunian objects are known to be in mean-motion
resonance with Neptune. We aim to describe their long-term orbital evolution
(both past and future) by means of a one-degree-of-freedom secular model. In
this paper, we focus only on objects with a semi-major axis larger than 50
astronomical units (au).
  Methods. For each resonant object considered, a 500 000-year numerical
integration is performed. The output is digitally filtered to get the
parameters of the resonant secular model. Their long-term (Giga-year) orbital
evolution is then represented by the level curves of the secular Hamiltonian.
  Results. For the majority of objects considered, the mean-motion resonance
has little impact on the long-term trajectories (the secular dynamics is
similar to a non-resonant one). However, a subset of objects is strongly
affected by the resonance, producing moderately-high-amplitude oscillations of
the perihelion distance and/or libration of the argument of perihelion around a
fixed centre. Moreover, the high perihelion distance of the object 2015 FJ345
is plainly explained by long-term resonant dynamics, allowing us to also deduce
its orbital elements at the time of capture in resonance (at least 15 million
years ago). The same type of past evolution is expected for 2014 FZ71.
