Multisubband transport of the two-dimensional electron gas (2DEG) in modulation-doped Al[sub 0.22]Ga[sub 0.78]N/GaN heterostructures has been investigated by means of magnetotransport measurements at low temperatures and high magnetic fields. It is found that the mobility of the 2DEG in the first subband in a triangular quantum well at the heterointerface decreases significantly, while the mobility of the 2DEG in the second subband increases, when the Al[sub 0.22]Ga[sub 0.78]N barrier is partially relaxed. Such behavior of the 2DEG mobility is explained by the nonuniformity of the piezoelectric polarization field at the heterointerface induced by the Al[sub 0.22]Ga[sub 0.78]N relaxation and strong interface scattering. Meanwhile, it is concluded that the scattering from the remote ionized donors is the main mechanism contributing to the quantum scattering time and responsible for the intersubband scattering in the quantum well at the heterointerface. [ABSTRACT FROM AUTHOR]