Magnetization data have been obtained for Nb−33%Zr 0.010‐in.‐diam wires carrying a transport currentIin a constant external longitudinal magnetic fieldHextand with a liquid‐helium bath temperature of 4.2°K. The variation of magnetization withIfor a constantHextdepends on the relative directions ofIandHext. WhenIis antiparallel toHext, the specimens were observed to become paramagnetic at a threshold current less than the experimental critical current and remain paramagnetic up to the critical current. A linear relationship between the threshold current and the external field forHext<500 G is observed.