Magnetic field observations on ISEE-1 and 2 in and near the neutral sheet about 20 Re down the near-Earth magnetotail reveal the occurrence of structures resembling magnetic flux ropes. Both electric field and fast plasma data show that these structures convect across the spacecraft at speeds of 200--600 km/s, and that they have scale sizes of roughly 3--5 Re. The rope axis orientation is across the tail, approximately in the -Y GSM direction. Their magnetic structure is strikingly similar to magnetic flux ropes observed in the Venus ionosphere, and to flux transfer events observed at the dayside magnetopause. The total field-aligned current within these ropes may approach a million amps. These structures may arise because of patchy reconnection within the plasma sheet, or may be tearing islands formed when the plasma sheet magnetic field has a cross-tail component. Plasma sheet flux ropes are not a common feature at ISEE orbital altitudes; this suggests that near-Earth neutral line formation within ISEE apogee (22 Re) may be equally rare.