  We develop a theory of nonlinear cosmological perturbations on superhorizon
scales for generic single-field inflation. Our inflaton is described by the
Lagrangian of the form $W(X,\phi)-G(X,\phi)\Box\phi$ with
$X=-\partial^{\mu}\phi\partial_{\mu}\phi/2$, which is no longer equivalent to a
perfect fluid. This model is more general than k-inflation, and is called
G-inflation. A general nonlinear solution for the metric and the scalar field
is obtained at second order in gradient expansion. We derive a simple master
equation governing the large-scale evolution of the nonlinear curvature
perturbation. It turns out that the nonlinear evolution equation is deduced as
a straightforward extension of the corresponding linear equation for the
curvature perturbation on uniform $\phi$ hypersurfaces.
