The influence of neutron irradiation on the amorphous Ti _40.7 Hf _9.5 Ni _44.8 Cu ₅ and Ti ₅₀ Ni ₂₅ Cu ₂₅ thin ribbons, their crystallization behaviour and martensitic transformations that occur after crystallization have been studied. The critical fluence value of 1⋅10 ¹⁹ cm ⁻² was found. If the fluence was 1⋅10 ¹⁹ cm ⁻² or less, the crystallization parameters and the temperatures of the martensitic transformation that took place alloy after crystallization hardly changed. Otherwise, a huge increase in the crystallization temperature and enthalpy occurred and the degradation of the martensitic transformation in crystallized samples was observed.