The magnetoresistance of undoped n-type GaAs has been measured at liquid-helium temperatures employing magnetic field strengths up to 140 kOe. The samples had electron concentrations between 1.7×1015 and 4.9×1015 cm-3 at 77°K. At low magnetic fields, negative magnetoresistance is observed. It is analyzed into a positive and a negative component. The latter is a function of H(T+θ), where H is the magnetic field strength, T is the temperature, and θ has a value close to 2°K for each sample. In high magnetic fields, above 30 kOe, the resistivity increases very strongly with magnetic field strength, in a manner similar to that when conduction is due to quantum-mechanical resonance jumping of electrons between donor impurities. To account for both the low-field and high-field magnetoresistance, we suggest that conduction takes place in a set of excited impurity states which are delocalized in zero or low magnetic field but become localized because of shrinkage of the wave functions when a high magnetic field is present.