Four essentially pure copper coins of Augustus (more than 99% copper) and four highly alloyed <i>sestertii</i> of the A.D. second century were analyzed by x-ray fluorescence (XRF) and studied metallographically. The coin surfaces were first cleaned and the analyzed by XRF; subsequently the coins were abraded, polished, and reanalyzed by XRF. This process was repeated five or six times. No concentration gradients were found within the coins, and standard deviations for iron, nickel, silver, tin, antimony, and lead usually were close to the standard counting errors. Agreement between the surface analyses and the interior analyses was very good for the pure copper coins, except for antimony. In spite of pronounced inhomogeneities found by metallography in the microstructures of the <i>sestertii</i>, very good reproducibility of analyses was obtained in the interiors of the coins. In spite of the very rough, highly corroded surfaces of three of the <i>sestertii</i>, the surface compositions determined by XRF in general were in fairly good agreement with the interior compositions except for lead. Also surface concentrations of tin and antimony tended to be somewhat low. For even highly inhomogeneous copper-based coins, XRF analyses on properly prepared surfaces of coins should be useful in solving numismatic problems.