  We consider general, non-linear curvature perturbations on scales greater
than the Hubble horizon scale by invoking an expansion in spatial gradients,
the so-called gradient expansion. After reviewing the basic properties of the
gradient expansion, we derive the conservation law for non-linear curvature
perturbations for an isentropic fluid. We also define the gauge-invariant
curvature perturbation under a finite shift of time-slicing, and derive the
non-linear genralization of the $\delta N$ formalism. The results obtained are
straight-forward generalisations of those already proven in linear perturbation
theory, and the equations are simple, resembling closely the first-order
equations.
