The paper commences by reviewing the methods adopted for the protection of overhead lines and transformers from the incidence of lightning. Itis then pointed out that in manycases it is not economic, and in others technically difficult, to provide sufficient line protection, so that transformers connected to such lines are likely to be subjected to transients having high voltage-amplitudes and high time-rates of voltage change. The question of transformer winding breakdown due to transients is then reviewed and evidence is brought forward to show that the important stresses are those between coils and turns and not those in the major insulation. The conclusion drawn is that transformers can advantageously be protected in most cases by those wave-flatteners which, under all conditions, permit only safe rates of voltage-change to exist at the terminals. Three representative wave-flatteners—condensers, inductance coils, and surge absorbers—are then discussed and equations are given which indicate the manner in which their performances are calculated, consideration being given to all degrees of lightningconditions, including those which cause flashover near the protected transformer. Then follows an experimental analysis of the axial stresses, and their reduction by the use of wave-flatteners, in various transformer windingsunder travelling-wave, travelling-wave flashover, and direct lightning-stroke conditions. Several transformers, differing in rating, mode of winding, natural frequency, and value of a. are employed. The results are presented in the form of gradient-distribution curves so that the relative performances, under various conditions, of the three kinds of flattener may be readily examined and the effects of changes in transformer constants compared. Inthe Appendix are derived the equations of the surge absorber.