  In this paper we consider second order perturbations of a flat
Friedmann-Lema\^{i}tre universe whose stress-energy content is a single
minimally coupled scalar field with an arbitrary potential. We derive the
general solution of the perturbed Einstein equations in explicit form for this
class of models when the perturbations are in the super-horizon regime. As a
by-product we obtain a new conserved quantity for long wavelength perturbations
of a single scalar field at second order.
