The softening of the lowest infrared active vibration which leads to the ferroelectric instability in perovskite crystals is currently explained in terms of mode-mode interactions.1 There exists, at the present time, no microscopic basis for the calculation of the coupling coefficients, which had to be taken as parameters of the theory. We show here that these interactions have the same origin as the strong Raman scattering observed in oxide perovskites, namely a non-linear anisotropic electron-ion interaction localized at the oxygen ion. This explains also why only oxide perovskites exhibit such a behaviour. We use a shell model with an anisotropic core-shell coupling at the oxygen ion, which includes a quartic term.2 The adiabatic interaction between electrons (shells) and phonons (cores) leads to an effective fourth order phonon-phonon interaction. The temperature dependence of all the phonons and in particular the ferroelectric soft mode is obtained within the self-consistent Hartree approximation. Th...