  Context. ABDoradus is the main system of the ABDoradus moving group. It is a
quadruple system formed by two widely separated binaries of pre-main-sequence
(PMS) stars: ABDor A/C and ABDor Ba/Bb. The pair ABDor A/C has been extensively
studied and its dynamical masses have been determined with high precision, thus
making of ABDor C a benchmark for calibrating PMS stellar models. If the orbit
and dynamical masses of the pair ABDor Ba/Bb can be determined, they could not
only play a similar role to that of ABDor C in calibrating PMS models, but
would also help to better understand the dynamics of the whole ABDoradus
system. Aims. We aim to determine the individual masses of the pair ABDor Ba/Bb
using VLBI observations and archive infrared data, as part of a larger program
directed to monitor binary systems in the ABDoradus moving group. Methods. We
observed the system ABDor B between 2007 and 2013 with the Australian Long
Baseline Array (LBA), at a frequency of 8.4 GHz in phase-reference mode.
Results. We detected, for the first time, compact radio emission from both
stars in the binary, ABDor Ba and ABDor Bb. This result allowed us to determine
the orbital parameters of both the relative and absolute orbits and,
consequently, their individual dynamical masses: 0.28+/-0.05 Msun and
0.25+/-0.05 Msun, respectively. Conclusions. Comparisons of the dynamical
masses with the prediction of PMS evolutionary models show that the models
underpredict the dynamical masses of the binary components Ba and Bb by 10-30%
and 10-40%, respectively, although they all still agree at the 2-sigma level.
Some of stellar models considered favour an age between 50 and 100 Myr for this
system, meanwhile others predict older ages. We also discuss the evolutionary
status of ABDor Ba/Bb in terms of an earlier double-double star scenario that
might explain the strong radio emission detected in both components.
