[en] The time-domain inverse problem of determining the three-dimensional parameter functions for the biisotropic dispersive medium is considered. Maxwell close-quote s equations are rewritten in terms of the tangential fields. Time domain wave-splitting of Maxwell close-quote s equations is applied to the total field that is generated by a dipole exterior to the scattering medium. The structure of the electromagnetic fields is analyzed, and the transport equations are given. The reconstruction condition is derived for a layer-stripping approach. copyright 1997 American Institute of Physics