Feynman diagrams for the NEGFs of electrons are developed here from the perturbation expansion in the case of electron–electron and electron–phonon interactions, assuming a phenomenological phonon Hamiltonian in the latter case. The corresponding diagrammatic expansion for the phonon NEGF in the case of the electron–phonon interaction is then developed. Finally, we consider cubic and quartic anharmonicity and develop the NEGF diagrammatic perturbation series in this case. As simple applications, renormalisation of phonons and the self-consistent phonon method are briefly discussed. The detailed theory presented here corresponds to the most general case of non-zero temperature and time dependence.