High-k dielectric stacks are regarded as a promising information storage media in the Charge Trapping Non-Volatile Memories, which are the most viable alternative to the standard floating gate memory technology. The implementation of high-k materials in real devices requires (among the other investigations) estimation of their radiation hardness. Here we report the effect of gamma radiation (60Co source, doses of 10 and 10 kGy) on dielectric properties, memory windows, leakage currents and retention characteristics of nanolaminated HfO2/Al2O3 stacks obtained by atomic layer deposition and its relationship with post-deposition annealing in oxygen and nitrogen ambient. The results reveal that depending on the dose, either increase or reduction of all kinds of electrically active defects (i.e., initial oxide charge, fast and slow interface states) can be observed. Radiation generates oxide charges with a different sign in O2 and N2 annealed stacks. The results clearly demonstrate a substantial increase in memory windows of the as-grown and oxygen treated stacks resulting from enhancement of the electron trapping. The leakage currents and the retention times of O2 annealed stacks are not deteriorated by irradiation, hence these stacks have high radiation tolerance.