EN
The influence of the magnetic field annealing on the magnetoimpedance effect has been investigated in rapidly quenched (Fe_{0.5}Ni_{0.5})_{78}Nb_{7}B_{15} monolayer and bilayer thin ribbons. The highest impedance ratio value (ΔZ/Z)_{max}=72% and the maximum field sensitivity η_{max}=12 %/Oe was obtained in the bilayer ribbon, annealed under longitudinal magnetic field at 773 K that exhibited nanocrystalline structure. The higher values of (ΔZ/Z)_{max} in bilayer ribbons, as compared to their monolayer counterparts, are attributed to the increased ratio of their thickness to the penetration depth.