We present the results of the experimental and theoretical studies of the low field mobility of two-dimensional electrons in the homoepitaxial AlGaN/GaN heterostructures and in the AlGaN/GaN heterostructures grown on SiC. We show that, at cryogenic temperatures, the temperature dependence of the mobility is primarily determined by the deformation potential scattering and that most of other important scattering mechanisms are temperature independent. We show also that two-dimensional (2D) and three-dimensional (3D) mobility models yield very close results. The analysis of the mobility dependence on the electron sheet density n
s shows two possible explanations of the non monotonic mobility versus carrier density dependence: i) the alloy/interface scattering and ii) transfer of the 2D electrons into 3D states in GaN. We present experimental data suggesting that for high 2D gas densities in the investigated structure grown on SiC the 2D-3D transition should take place and might be responsible for the mobility decrease at high electron sheet densities.