  Using numerical integrations, we find that the orbital eccentricity of
Saturn's moon Iapetus undergoes prominent multi-Myr oscillations. We identify
the responsible resonant argument to be
$\varpi-\varpi_{g5}+\Omega-\Omega_{eq}$, with the terms being the longitudes of
pericenter of Iapetus and planetary secular mode $g_5$, Iapetus's longitude of
the node and Saturn's equinox. We find that this argument currently (on a
$10^7$~yr timescale) appears to librate with a very large amplitude. On longer
timescales, the behavior of this resonant angle is strongly dependent on the
resonant interaction between Saturn's spin axis and the planetary mode $f_8$,
with long-term secular resonance being possible if Saturn's equinox is
librating relative to the node of the $f_8$ eigenmode. We present analytical
estimates of the dependence of the resonant argument on the orbital elements of
Iapetus. We find that this Iapetus-$g_5$ secular resonance could have been
established only after the passage of Iapetus through the 5:1 mean-motion
resonance with Titan, possibly in the last Gyr. Using numerical simulations, we
show that the capture into the secular resonance appears to be a
low-probability event. While the Iapetus-$g_5$ secular resonance can
potentially help us put new constraints on the past dynamics of the Saturnian
system, uncertainties in both the spin axis dynamics of Saturn and the tidal
evolution rate of Titan make it impossible to make any firm conclusions about
the resonance's longevity and origin.
