Voyager's post-encounter trajectory at Neptune allows the directions of the magnetic field in the magnetosheath produced by the draping of the typical interplanetary field and by alignment with the magnetotail to be distinguished. Changes of the field from the draped to the magnetotail-aligned direction accompanied by decreases of plasma velocity, density, and temperature, observed at intervals of approximately a Neptunian day, are consistent with the assumption that Voyager repeatedly encountered a plasma mantle region extending well into the magnetosheath and modulated by the rotation of the planet's magnetic dipole. Other interpretations are either implausible or inconsistent with the observations. Previously reported periodic velocity decreases in the magnetosheath of Uranus can be interpreted in the same way. Extended plasma mantles may thus be a general property of planetary magnetospheres interacting with the magnetized solar wind. Analogous effects at Earth cannot yet be observed because of lack of suitable spacecraft missions, but their existence is suggested by theoretical arguments. ¿ American Geophysical Union 1990