A ``displaced linear branch'' has been observed in the volt‐ampere characteristics of square (1 × 1‐mm) Sn&sngbnd;Ox&sngbnd;Sn and Pb&sngbnd;Ox&sngbnd;Pb Josephson junctions. The slope of the linear branch is independent of magnetic field and independent of temperature below 2.2°K. It is suggested that this effect can be attributed to internal flux motion.