  High-order multiple (triple and beyond) systems are relatively common. Their
interaction with circumstellar and circumbinary material can have a large
impact on the formation and evolution of planetary systems and depends on their
orbital properties. GG\,Tau and UX\,Tau are two pre-main sequence high-order
multiple systems in which the tightest pair has a projected separation of
$\approx5$--20\,au. Characterizing precisely their orbits is crucial to
establish their long-term stability, to predict the dynamics and evolution of
circumstellar matter, and to evaluate the potential for planet formation in
such systems. We combine existing astrometric measurements with previously
unpublished high-resolution observations of the GG\,Tau\,Ab and UX\,Tau\,B
pairs and perform Keplerian orbital fits. For GG\,Tau\,Ab the data presented
here represent the first detection of orbital motion. For both systems they
yield dramatic increases in orbital coverage ($\gtrsim60\%$ and $\approx100\%$
for UX\,Tau\,B and GG\,Tau\,Ab, for orbital periods of $\approx32$ and
$\approx8$\,yr, respectively) and allow us to obtain well-constrained orbital
fits, including dynamical masses with $\lesssim10\%$ and $\lesssim7\%$ random
and systematic uncertainties. We find that both GG\,Tau\,A and UX\,Tau\,A--B
likely form stable hierarchical systems, although one possible deprojection
solution for GG\,Tau is strongly misaligned and could experience von
Zeipel-Lidov-Kozai oscillations. We further find that the UX\,Tau\,B orbit is
much more eccentric than the GG\,Tau\,Ab one, possibly explaining the lack of
circumstellar material in the former. The newly-determined orbits revive the
question of the dynamical fate of gas and dust in these two hierarchical
systems and should spur new dedicated simulations to assess the long-term
evolution of the systems and the dynamical perturbations imposed by the close
binaries they host.
