This letter reports the giant magnetoimpedance ͑GMI͒ effect and its magnetic response in optimized Co 70 Fe 5 Si 15 Nb 2.2 Cu 0.8 B 7 amorphous and Fe 71 Al 2 Si 14 B 8.5 Cu 1 Nb 3.5 nanocrystalline ribbons. At a given frequency of 5 MHz, the largest GMI ratios of 513% and 640% were observed for the Co-based amorphous and Fe-based nanocrystalline samples, respectively. More interestingly, the magnetic response reached the largest value of 144%/Oe at the frequency of 4 MHz for the Co-based amorphous sample and of 40%/Oe at the frequency of 5 MHz for the Fe-based nanocrystalline sample. This is ideal for high-frequency and high-performance GMI-based sensor applications. The skin effect model was used to interpret the obtained results of GMI in connection with the magnetic-field and frequency dependences of the longitudinal permeability.