Details of a theoretical model to describe the properties of the D^- centre in GaAs/GaAlAs multi-quantum-well (MQW) Systems in the presence of a magnetic field are presented. It is based on a matrix diagonalization procedure that was developed by the present authors earlier for the D⁰ centre in the same MQW systems. Tie results obtained are compared with published experimental data obtained from far-infrared magnetotransmission and photoconductivity measurements. Good agreement is obtained with these data for samples with relatively wide well widths. The calculations show that the dominant transition is between the mod ls2) ground state and the mod 1s2p₊) excited state, and indicate that the original suggestion that the main transition is of an ionizing type involving a Landau level is probably invalid. Qualitative agreement is also obtained between the calculations and the results of experiment performed on samples with narrower well widths.