The effect of magnitude of tensile stresses (σ) applied to the (Fe0.7Co0.3)88Hf2W2Mo2Zr1B4Cu1 alloy with refractory-metal additions during its nanocrystallization at 620°C for 20 min on the magnetic properties, structure, and thermal stability of the alloy is studied. It has been found that, during the nanocrystallization of the alloy under the effect of tensile stresses of 6–250 MPa, longitudinal magnetic anisotropy with an easy magnetization axis parallel to the long size of ribbon is induced in the alloy. The thermal stability of magnetic properties of the alloy under study has been shown to be determined by the thermal stability of induced magnetic anisotropy and to depend on the magnitude of tensile stresses applied during nanocrystallizing annealing (NA). The better thermal stability of magnetic properties has been observed for the alloy subjected to NA at σ = 170 MPa. After annealing at 570°C for 25 h, the magnetic properties of the alloy are unchanged.