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This paper presents the results of experimental tests performed with an impulse voltage of short tail (STLI: 1.2/4 ??s), similar to lightning-induced overvoltages, on composite insulators used in the electric traction lines. The characteristics of volt-time breakdown under STLI waves are shown and compared with the characteristics obtained under standard lightning impulse (LI:1.2/50 ??s). Models based on the disruptive effect, as proposed by Kind and Chowdhuri, are considered and applied in order to reproduce the volt-time characteristics under standard and nonstandard lightning voltages. The application viability of these models to tested insulators is considered and discussed and the accuracy in their reproduction is evaluated. It is demonstrated that the Kind model, calibrated with a suitable selection of the parameters using standard flashover data (LI), is able to estimate the response of the insulators to the short tail lightning impulses (STLI) with satisfactory accuracy.