Abstract-Several experimental time-domain EM induction instruments have recently been developed for unexploded ordnance (UXO) detection and characterization that use multiple transmitting and receiving coil combinations. One such system, the US Geological Survey's ALLTEM system, is unique in that it measures both the electrodynamic response (i.e., induced eddy currents) and the magneto-static response (i.e., induced magnetization). This allows target characterization based on the dyadic polarizability of both responses. This paper examines the numerical response of the ALLTEM instrument due to spheroidal, conductive, and permeable UXO targets; and to conductive and optionally viscous magnetic earth. An inversion scheme is presented for spheroidal targets that incorporates fully polarimetric measurements for both magneto-static and electro-dynamic excitations. The performance of the inversion algorithm is evaluated using both simulated and surveyed data. The results are examined as a function of the number of coil combinations, number of instrument locations, and uncertainty in sensor location and orientation. Results from the specific cases tested (prolate spheroids lying horizontally) show that 1) that collecting data from more than 12 sensor locations or from more than four coil combinations reduced the chances that inversion solutions would be from a local minimum, and 2) that uncertainties in position greater than 3 cm or in orientation greater than 10 degrees cause errors in the estimated spheroid principal lengths of greater than 100%. Soil conductivities less than 1 S/m contribute negligible interference to the target response, but viscous magnetic soils with permeabilities greater than 10 −6 MKS units do cause detrimental interference.