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 Fe4.3Co68.2Si12.5B15 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 Fe7.5Co67.5Si15B10 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.