The paper reports measurements of the strains and electrical resistance of a TiNi shape-memory alloy under irradiation in the low-temperature helium circuit of a nuclear reactor. Irradiation of the alloy in martensitic state at 170 K revealed that the transition temperatures from cubic to rhombohedral and from rhombohedral to monoclinic phase decrease exponentially with increasing dose. No change in the shape-memory effects and transformation plasticity was observed up to a dose of 6.7×10²²n/m². Keeping the sample at 340 K without irradiation restores (increases) partially the transition temperatures. The relations observed can be assigned to a change in the degree of long-range order in the lattice caused by neutron irradiation.