The paper is essentially a short critical résumé of the factors which, in general, determine the security of high-voltage a.c. overhead-line transmission systems with, in addition, a description of methods which provide a logical basis for the efficient selection of insulation levels.Transient over-voltages are the main source of danger to overhead-line insulation; they may be of internal origin, but lightning strokes are the major hazard, particularly in oversea countries where lightning is prevalent. Lightning phenomena are therefore considered; statistical data on lightning currents, stroke frequency and other variables are included. The problem of shielding by earth wires and the importance in this connection of tower footing resistance are discussed.A description of the characteristics of line insulation is given; this includes data on power-frequency and impulse tests, flashover voltages, atmospheric influences, deterioration, use of wood poles, and other related matters.The selection of insulation levels involves careful consideration of the foregoing factors with, in addition, a means of estimating line reliability or probable outage frequency. Two methods which have been developed for predicting line performance under lightning conditions are described and compared, and their application is illustrated by numerical examples.