  We show that inflation which is dominated by the D-term density avoids the
`slow-roll' problem of inflation in supergravity. Such an inflationary scenario
can naturally emerge in theories with non-anomalous or anomalous U(1) gauge
symmetry. In the latter case the scale of inflation is fixed by the
Green--Schwarz mechanism of anomaly cancellation. The crucial point is that the
(super)gravity-mediated curvature of all the scalar fields (and, in particular,
of the inflaton), which in the standard F-dominated case is of the order of the
Hubble parameter, is absent in the D-term inflation case. The curvature of
moduli and of all other flat directions during such an inflation crucially
depends on their gauge charges.
