The electrical properties, electroluminescence (EL) power output and deep trap spectra were studied before and after 5 MeV electron irradiation of near-UV single-quantum-well (SQW) light-emitting diodes (LED) structures differing by the presence or absence of InAlN superlattice underlayers (InAlN SL UL). The presence of the underlayer is found to remarkably increase the EL output power and the radiation tolerance of LEDs, which correlates with a much lower and more slowly changing density of deep traps in the QW region with radiation dose, and the higher lifetime of charge carriers, manifested by higher short-circuit current and open-circuit voltage in current-voltage characteristics under illumination. The observed phenomena are explained by the capture of native defects segregated at the growing surface by In atoms in the underlayer which traps them in the underlayer and prevents their penetration into the QW region.