Considerable recent research on the draping of the interplanetary magnetic field (IMF) about the ionospheres of comets and Venus and about the Earth's magnetosphere, as well as draping of magnetospheric fields about Io's ionosphere and plasmoids, has indicated the fundamental and prevalent nature of this process. In this paper we consider the possibility of magnetic field draping about fast coronal mass ejections (CMEs) which propagate into the outer heliosphere through slower moving, quiescent solar wind. In particular, when this velocity difference is appreciably greater than the local Alfv¿n speed, draping should produce extended magnetotaillike configurations somewhat analogous to those observed behind Venus and comets. For CMEs, however, such tails would point sunward and form on scales comparable to these large ejecta. In the draped magnetotial regions sunward of fast CMEs in the outer heliosphere the IMF should be relatively radial, in contrast to the generally transverse orientation of the Parker spiral there. Low transverse flow velocities in the draped regions just upstream from fast CMEs suggest that swept-up interplanetary magnetic flux is hung up on these large structures (~1 AU in transverse dimension at 1 AU) for many days. We have searched for evidence of magnetic field draping about fast CMEs and the existence of large draped magnetotails in the outer heliosphere by examining the Pioneer 11 data set between 6.9 and 9.4 AU. Several events consistent with such structures have been found, and two are displayed in the study. ¿ American Geophysical Union 1988