AlGaN/GaN heterostructures with two-dimensional electron gas (2DEG) grown by metal organic chemical vapor deposition were investigated by photoluminescence (PL) spectroscopy. The PL spectra of these heterostructures contain an unusual band assigned to quasi-donoracceptor recombination transitions (Q-DAP) from small-size regions of the GaN layer with perturbed conduction and valence band edges. The Q-DAP band dominates the delayed nonstationary PL spectra; its energy position changes strongly with time after the excitation pulse (up to 160 meV within 10 μs). The Q-DAP band intensity decreases under continuous excitation during tens of minutes. The appearance of the Q-DAP band is accompanied by a rise in the intensity of the PL bands associated with 2DEG.