The influence of structure-phase features and electric current modes on the electroplastic effect (EPE) revealed at tension for coarse-grained, nanocrystalline and amorphous TiNi-based alloys is investigated. Grain-size refinement up to nanoscale and amorphization in alloys lead to decreases or even full disappearance of EPE. In nanocrystalline alloys with reverse thermoelastic martensite transformation, the introduction of current pulses suppresses downwards stress jumps induced by the EPE and causes active upwards stress jumps connected with the shape memory effect (SME).