A generalised form of recombination, wherein an offspring can be formed from any of the genetic material of the parents, is analysed in the context of a two-locus recombinative GA. A complete, exact solution, is derived, showing how the dynamical behaviour is radically different to that of homologous crossover. Inversion is shown to potentially introduce oscillations in the dynamics, while gene duplication leads to an asymmetry between homogeneous and heterogeneous strings. All non-homologous operators lead to allele "diffusion" along the chromosome. We discuss how inferences from the two-locus results extend to the case of a recombinative GA with selection and more than two loci.