  Inflation may have been driven by a component which violated the Null-Energy
Condition, thereby leading to {\it super inflation}. We provide the formalism
to study cosmological perturbations when such a component is described by a
scalar field with arbitrary Lagrangian. Since the background curvature grows
with time, gravitational waves always have a blue spectrum. Scalar
perturbations may also have a blue spectrum, {\em albeit} in single field
models. We apply our formalism to the case of phantom inflation with an
exponential potential (whose pole-like inflationary stage is an attractor for
inhomogeneous cosmological models for any value of the potential slope). We
finally compare the predictions of super inflation with those of standard
inflation stressing the role of gravitational waves.
