The controllable annealing of amorphous Ti2NiCu ribbons by a pulsed electric current was developed, and samples with different fractions of crystalline phase were obtained. The samples’ structure was studied using high-resolution electron microscopy. Annealing conditions allowing us to obtain an amorphous nanocrystalline structure with grain sizes of less than 10 nm were determined. Conditions for obtaining samples with the two-wave shape memory effect were found. A prototype micromanipulator was designed and successfully tested.