We present an astrometric analysis of the binary systems AB DorA/ABDor C and ABDor Ba /AB Dor Bb. These two systems of well-known late-type stars are gravitationally associated and they constitute the quadruple ABDoradus system. From the astrometric data available at different wavelengths, we report: (i) a determination of the orbit of ABDor C, the very low mass companion to ABDorA, which confirms the mass estimate of 0.090 Mo reported in previous works; (ii) a measurement of the parallax of ABDorBa, which unambiguously confirms the long-suspected physical association between this star and ABDor A; and (iii) evidence of orbital motion of ABDor Ba around ABDorA, which places an upper bound of 0.4 Mo on the mass of the pair ABDorBa /ABDor Bb (50% probability). Further astrometric monitoring of the system at all possible wavelengths would determine with extraordinary precision the dynamical mass of its four components.