Multistep current annealing (CA) treatments were performed on amorphous FINEMET-type Fe-Cu-V-Si-B, as well as on a novel Fe-Al-Ga-P-C-B alloy with a large supercooled liquid region, in order to optimize their magnetotransport properties. On-line and post-annealing electrical resistivity measurements, DSC, XRD and Mossbauer spectroscopy were used for characterization of structural changes evolved during CA treatments. Results on magnetoresistance (MR) and magnetoimpedance (MI) effects after CA in ribbon samples with relaxed amorphous as well as precipitated nanocrystalline structure are presented. Significant improvement in MI-response after CA up to Delta Z/Z approximate to 50% was recorded at frequencies 2-3 MHz. The highest MI-element sensitivity was found for low magnetic field intensity where values of about 6 %/kA/m for samples of Fe-Al-Ga-P-C-B alloy were attained.