Conflicting reports of large magnetoresistive and magnetoinductive effects in amorphous FeCoSiB wires and ribbons prompted the impedance measurements reported here. The spectra (0≤f≤3.2 MHz) were obtained at room temperature using a commercial impedance analyzer both as functions of axial magnetic field (-140<HA<140 Oe) and sense current (1≤Irms≤60 mA). The phase shift due to the test leads was carefully measured and subtracted from the raw data to resolve the spectra into resistive R(f) and reactive X(f) components. We find for the Fe4.3Co 68.2Si12.5B15 wire (120 μm diameter) and ribbon (20 μm thick) that both R(f) and X(f) depend strongly on frequency and magnetic field. For HA=0, each component increases monotonically with frequency, with R(f=0)≊1 Ω/cm and X(f=0)=0. In high fields (HA=140 Oe), R(f) and X(f) are nearly frequency independent. The field-dependent response is sharply peaked about HA=0; the full width at half maximum is FWHM≤20 Oe, typically. The change in R(f) and X(f) between these two extremes is extraordinarily large; 4.5 Ω/cm at f=1 MHz is a typical value for the wire. The sensitivity of the magnetoresistive response is 44% of the dc resistance per Oe for f=1 MHz. Qualitatively similar phenomena were observed for the Fe7.5Co67.5Si 15B10 ribbon, although the field and frequency dependences of the spectra are less pronounced than for the wire. We discuss a model which describes the spectra quantitatively, using classical electrodynamics.