Detailed measurements of voltage–current (E–J) characteristics have revealed a distinct low level resistive tail for silver‐sheathed (Bi,Pb)2Sr2Ca2Cu3O10 superconducting tapes. The residual tail is observed at very low voltage (E≤10−8–10−7 V/cm) of the E–J curves and can be described by E∝(J−Jc′)n, where Jc′ is a field and temperature dependent critical current and n=1.0–1.2. The dynamic resistivity is, typically, in the range of 10−13 Ω cm, but could be as high as 10−11 Ω cm in some specimens. This residual resistance can be induced by a severe thermal cycling treatment, although it may also be intrinsic, i.e., as‐grown, to some of the specimens. © 1995 American Institute of Physics.