A new hybrid technique, entirely formulated in the time domain, has been developed and used to study small radiating sources close to large but finite scatterers. It combines a rigorous method; the finite-difference time-domain (FDTD) method, with an asymptotic method, the time-domain physical-optics (TDPO) method. Numerical examples are performed to validate the principle of the new approach and demonstrate its higher computation performances compared to the classical FDTD algorithm. (C) 1999 John Wiley & Sons, Inc.