The authors fabricated and measured cylindrical superconducting current leads composed of a Y/sub 1/Ba/sub 2/Cu/sub 3/O/sub 7/ (YBCO) and Bi/sub 2-x/Pb/sub x/Sr/sub 2/Ca/sub 2/Cu/sub 3/O/sub 10/ (Pb-BSCCO) that were approximately 20 cm long and 1 cm/sup 2/ in cross section. A steady-state, DC, critical current of 170 (230) A at a temperature of 77 K was measured for YBCO (Pb-BSCCO) using a voltage criterion of 2*10/sup -7/ V ( rho =8*10/sup -10/ Omega -cm). This current was limited by the current-induced self-magnetic field. At a temperature of 63 K this current increased to approximately 390 (465) A. The character of the magnetic field dependence of the critical current and shape of the current-induced voltage curves are different for the two materials.