The transient electromagnetic response (vertical and horizontal components of dB/dt) of a large polygonal transmitting loop on a layered earth is calculated using a nested interpolation scheme based on the dipole-dipole response function. The frequency-domain field of a vertical magnetic dipole is inverse Laplace transformed into the time domain, for selected values of the Hankel transform variable, using the Gaver-Stehfest method. After interpolation, the result is inverse Hankel transformed (for selected values of distance) using digital filters. Interpolating over distance allows integration of the dipole response over the area of one or more transmitting loops. An interpolation over time gives the step-current response, which in turn is convolved with the transmitter-receiver characteristics to yield the system response. This method allows robust calculation of several transmitting loops (with different signal parameters) and several receiver positions in little more time than that required for one loop with one receiver. The computation time for the single transmitter-receiver response can be decreased by analytical integration of the Bessel function over the transmitter loop area before performing the inverse Hankel transform. Since this procedure precludes the use of standard digital filters for the inverse Hankel transform, it is not efficient for multireceiver computations.