The resistance of amorphous W-Re wires between 2 and 20°K has been measured. Wires with a resistance of approximately 10 k show a different temperature dependence from that of wires with a resistance of over 200 k. The latter show a relative increase in resistance as the temperature is decreased or the magnetic field is increased. These wires also show an anomalous dependence of resistance on width and length. These results are discussed in the perspective of Thouless's suggestion of maximum metallic resistance. © 1980 The American Physical Society.