The effect of neutron irradiation on the electrical properties of undoped n-AlGaN/GaN heterostructures is reported. The two-dimensional electron-gas (2DEG) mobility starts to decrease at neutron doses above 1014 cm-2, while the 2DEG concentration slightly increases at low doses and decreases dramatically for doses higher than 2.5×1016 cm-2. The result is that the mobility/concentration product (a figure of merit for transistors) starts to decrease appreciably after the dose of 1015 cm-2. Capacitance-voltage and admittance spectroscopies, indicate that tunneling of electrons into the states near Ec-0.21 eV in AlGaN is a serious factor when cooling down the virgin or lightly irradiated samples. For heavily irradiated samples the states in AlGaN are close to 0.3 and 0.45 eV, respectively, from the bottom of the conduction band. Deep-level spectroscopy measurements reveal the presence of hole traps with apparent activation energies of 0.18 and 0.21 eV for lightly irradiated samples and deeper hole traps with activation energies of 0.6 and 1 eV in heavily irradiated samples.