  Erupting filaments are sometimes observed to undergo a rotation about the
vertical direction as they rise. This rotation of the filament axis is
generally interpreted as a conversion of twist into writhe in a kink-unstable
magnetic flux rope. Consistent with this interpretation, the rotation is
usually found to be clockwise (as viewed from above) if the post-eruption
arcade has right-handed helicity, but counterclockwise if it has left-handed
helicity. Here, we describe two non--active-region filament events recorded
with the Extreme-Ultraviolet Imaging Telescope (EIT) on the {\it Solar and
Heliospheric Observatory} ({\it SOHO}), in which the sense of rotation appears
to be opposite to that expected from the helicity of the post-event arcade.
Based on these observations, we suggest that the rotation of the filament axis
is in general determined by the net helicity of the erupting system, and that
the axially aligned core of the filament can have the opposite helicity sign to
the surrounding field. In most cases, the surrounding field provides the main
contribution to the net helicity. In the events reported here, however, the
helicity associated with the filament ``barbs'' is opposite in sign to and
dominates that of the overlying arcade.
