The magneto-optical spectrum of the shallow donors in n-GaAs is studied using a far-infrared laser at photon energies greater than the binding energy of the donors. The transitions from the (1s) ground state into the Landau levels are not observed but, instead, series of transitions from the ground state into donor states associated with the individual Landau levels. The strongest series corresponds to the (000)-(0N0) transitions and the second strongest series to (000-0N2) transitions where N is the index of the Landau level involved (and where the high-field notation is employed). The corresponding low-field notation is 1s-2p₊, 1s-3d₊₂, 1s-4f₊₃, 1s-5g₊₄ etc. for the strongest series which can be followed up to the N=17 Landau level. Central cell structure due to the presence of several different donors can be observed on many of the lines associated with the N=1 and N=2 Landau levels. The 1s-3p₊ transition can be used to determine chemical shifts accurately for the donor species present, as this line avoids the overabsorption effects which can distort the stronger 1s-2p₊ line. A few weak lines remain unidentified.