The convolution kernels of a Volterra series give a generalization of impulse responses to the case of weakly nonlinear input-to-output systems. In acoustics, this formalism has yet been used to solve, e.g. the problem of a nonlinear string excited by a force f(t) (considered as the input), spatially distributed by a time invariant function. In this paper, we propose a similar generalization for the case of Green functions in order to tackle inputs that depend on both the space and the time variables. The method to derive the "Green-Volterra" kernels is described and its application to the string is presented.