The effect of stress-induced martensite aging on the microstructure, viscoelastic properties, and one-way and two-way shape memory effect in high-temperature Ni50.2Ti37.3Hf12.5 aged polycrystals in tension was investigated. Stress-induced martensite aging for 6 h resulted in significant changes in the viscoelastic properties of the polycrystals. The elastic module of the martensite and austenite increased (by a factor of two), and a large softening of the elastic module and the growth of internal friction by 30% during MT was observed. Aging in martensite leads to the induction of a two-way shape memory effect with a strain of 1.7%, whose degradation is related to the microstructural change. It is established that both the value and the stability of the high-temperature two-way shape memory effect are defined by the time of the stress-induced martensite aging and the maximum value and stability were observed at an aging time of 6 h.