The magnetoimpedance (MI) effect in Fe73.5Si13.5B9Nb3Cu1 melt-spun amorphous ribbons has been studied in the frequency range (1-500 MHz). Isothermal heating treatments in a furnace have been employed to nanocrystallize the ribbons (1 h at 565 degrees C in a vacuum of 10(-3) mbar), while other samples were annealed at lower temperatures (400 and 475 degrees C during 1 h), in order to evaluate the influence of the annealing temperature on the MI effect. The high-frequency impedance was measured using a technique based on the reflection coefficient measurements of a specific transmission line by using a network analyzer. Frequency dependence of the MI ratio, DeltaZ/Z, and both resistive, DeltaR/R, and reactive, DeltaX/X, components of magnetoimpedance were measured in the amorphous and annealed states, at different temperatures. A maximum value of the MI ratio of about 50% at a driving frequency of 18 MHz is obtained in the nanocrystalline (annealed at 565 degrees C) ribbon. Maxima for DeltaR/R of about 81% at 85 MHz and DeltaX/X around 140% at 5 MHz were also achieved. It is revealed that the microstructural evolution in the nanocrystalline sample leads to a magnetic softening, an optimum domain structure and a permeability which is sensitive to frequency and applied magnetic field, generating a large MI response.