  We develop a theory of nonlinear cosmological perturbations on superhorizon
scales for a multi-component scalar field with a general kinetic term and a
general form of the potential in the context of inflationary cosmology. We
employ the ADM formalism and the spatial gradient expansion approach,
characterised by O(\epsilon^2), where \epsilon=1/(HL) is a small parameter
representing the ratio of the Hubble radius to the characteristic length scale
L of perturbations. We provide a formalism to obtain the solution in the
multi-field case. This formalism can be applied to the superhorizon evolution
of a primordial non-Gaussianity beyond the so-called \delta N formalism which
is equivalent to O(\epsilon^0) of the gradient expansion. In doing so, we also
derive fully nonlinear gauge transformation rules valid through O(\epsilon^2).
These fully nonlinear gauge transformation rules can be used to derive the
solution in a desired gauge from the one in a gauge where computations are much
simpler. As a demonstration, we consider an analytically solvable model and
construct the solution explicitly.
