  Polarized nuclei are a powerful tool in nuclear spin studies and in searches
for beyond-the-standard model physics. Noble-gas comagnetometer systems, which
compare two nuclear species, have thus far been limited by anomalous frequency
variations of unknown origin. We studied the self-interactions in a
$^3$He-$^{129}$Xe system by independently addressing, controlling and measuring
the influence of each component of the nuclear spin polarization. Our results
directly rule out prior explanations of the shifts, and demonstrate
experimentally that they can be explained by species dependent
self-interactions. We also report the first gas phase frequency shift induced
by $^{129}$Xe on $^3$He.
