The techniques of scanning tunneling microscopy (STM) and scanning tunneling potentiometry (STP) have been used simultaneously to study the electromigration behavior of a gold covering (1-2 nm) on a carbon thin film surface over 200 h. The applied lateral direct-current (dc) voltage gradient corresponded to a mean current density j = 1 X 10(4) A/cm2. The topography of the surface was measured by alternating-current (ac) tunneling. The spatial variation of the electric potential was determined from the dc component of the tunneling current. The surface was studied continuously without any interruptions of the tunneling contact on an area of about (2.3 mum)2. The topography and the potential distribution are drastically changed during this long-range experiment. In considerations of the local potential drop we were able to characterize the thickness of the Au covering. In the first stage of the experiment (t<60 h) the STM/STP results indicate a flux of Au atoms from the anode to the cathode. After that coalescence and faceting of the Au covering were observed. We assume that the surface is adjusted to a minimum surface energy configuration, involving in most cases (111) facets.