Three-wave interaction in a possibly strongly inhomogeneous plasma was considered in Paper II. These results are now generalized in order to treat also time-dependent periodic systems. The coupled mode equations as given in this paper are applicable to a very large class of unperturbed systems including those in Paper II and plasmas with self-consistent or in external oscillating field and also plasmas with some crystal symmetry in space-time. In the particular case when the relativistic Vlasov equation is used to describe the plasma we give symmetric expressions for the coupling coefficients such that the Manley–Rowe relations follow if wave–particle interaction is neglected.