A theoretical study is made of the energy levels of shallow donors in bulk GaAs and in GaAs/AlGaAs superlattices in an external magnetic field. The influence of magneto-polarons on these energy levels is studied within second-order perturbation theory. Special attention is paid to the resonant polaron interaction, and the importance of band non-parabolicity at high magnetic fields is also shown. Once-electron as well as two-electron bound states of the donor are investigated. Our results are in good agreement with available experimental far-infrared optical data of the different transitions within the above systems.