One of the weaknesses of the nondestructive determination of fineness in coins minted in binary silver-copper alloy is the thinness of the thickness analyzed. We present a new method, fast neutron activation analysis with neutrons produced by a cyclotron, which permits a nondestructive and total measurement of silver. A comparison with other chemical and atomic analytical methods used on Roman coins shows the interest of fast neutron activation analysis. Moreover, this method is applied to the study of second and third centuries Roman medals minted in silver, billon, and bronze. -- AATA