Abstract: A method of TIG welding with alternating current with a welding apparatus (10) which is arranged in such a manner that the polarity of the welding current is controlled by an electronic control circuit (20), which is also arranged so that it continuously registers whether or not the arc is lit, and in that the welding apparatus comprises a controllable inverter (16) and means for re-igniting the arc in the positive period, and arranged so that the length of the positive period is shortened if the arc is not re-ignited in the positive period. The invention also relates to a welding apparatus which can be equipped with a logical circuit or a programmable circuit which instantly ensures that the positive welding period is shortened if the arc is not re-ignited in this period.