The mechanism of spin–phonon coupling (SPC) in high-TC copper oxides is explored from band calculations on La(2−x)SrxCuO4 and HgBa2CuO4 systems. The LMTO band calculations, based on the local density approximation, are made for cells containing frozen phonon displacements and/or spin waves within the CuO plane. The virtual crystal approximation is used for studies of hole doped systems. The main result is that phonons are favorable for spin waves and vice-versa, and that pseudogaps appear naturally in the band structures of striped materials with strong SPC. The qualitative results are compatible with many observations showing that the properties of high-TC superconductors depend both on lattice interactions and magnetic fluctuations. The band results are used to model various properties, mainly of the normal state, such as isotope effects, pseudogaps, Fermi surface broadening, T-dependence of the pseudogap, phonon softening and some aspects of superconductivity. The possibility of perpendicular SPC is investigated, partly by the use of a nearly free electron model.