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: ABDorA/C and ABDor Ba/Bb. The pair ABDorA/C has been extensively studied and its dynamical masses have been determined with high precision, thus making of ABDorC 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 ABDorC 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±0.05M_sun and 0.25±0.05M_sun, 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 ~30 and 40%, respectively, although they all still agree at the 2-sigma level. The same stellar models favour an age between 50 and 100 Myr for this system. 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.