Here we report on the magnetic and magnetoelastic properties of a family of magnetic nanocrystalline wires with diameters in the range 10-30 μm, obtained by successive cold drawings of FINEMET amorphous wires precursors (105 μm in diameter) prepared by in-rotating-water spinning. Their unique magnetic properties are discussed considering the stresses induced during preparation and cold drawing, the stresses relief following annealing, the annealing-induced structural transformations (e.g., nanocrystallization) and the corresponding changes in the magnetic anisotropy.