Transient magnetic fields are analyzed in the time domain by using the finite-element method (FEM) in space and the finite-difference method in time. Conductive regions are eliminated from the domain under examination by imposing impedance boundary conditions on the surfaces separating conductive and nonconductive regions. In the time domain, the impedance boundary conditions are represented by a convolution integral in which the transient surface admittance appears whose expression can be obtained analytically by the inverse Laplace transform. A 2-D numerical procedure is presented for the solution of the integral equation deriving from the application of surface impedance boundary conditions. >