  We study higher order corrections in new minimal supergravity models of a
single scalar field inflation. The gauging in these models leads to a massive
vector multiplet and the D-term potential for the inflaton field with a
coupling g^{2} ~ 10^{-10}. In the de-Higgsed phase with vanishing g^2, the
chiral and vector multiplets are non-interacting, and the potential vanishes.
We present generic manifestly supersymmetric higher order corrections for these
models. In particular, for a supersymmetric gravity model -R+ R^2 we derive
manifestly supersymmetric corrections corresponding to R^n. The dual version
corresponds to a standard supergravity model with a single scalar and a massive
vector. It includes, in addition, higher Maxwell curvature/scalar interaction
terms of the Born-Infeld type and a modified D-term scalar field potential. We
use the dual version of the model to argue that higher order corrections do not
affect the last 60 e-foldings of inflation; for example the \xi R^4 correction
is irrelevant as long as \xi< 10^{24}.
