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Dislocation-free high-quality AlGaN/GaN heterostructures have been grown by molecular-beam epitaxy on semi-insulating bulk GaN substrates. Hall measurements performed in the 300 K–50 mK range show a low-temperature electron mobility exceeding 60 000 cm2/V s for an electron sheet density of 2.4×1012 cm−2. Magnetotransport experiments performed up to 15 T exhibit well-defined quantum Hall-effect features. The structures corresponding to the cyclotron and spin splitting were clearly resolved. From an analysis of the Shubnikov de Hass oscillations and the low-temperature mobility we found the quantum and transport scattering times to be 0.4 and 8.2 ps, respectively. The high ratio of the scattering to quantum relaxation time indicates that the main scattering mechanisms, at low temperatures, are due to long-range potentials, such as Coulomb potentials of ionized impurities.