The system according to the invention allows plastic bags to be very securely sealed by welding, using a compact apparatus. The device uses the multiplexing of the electrical energy sent into the heating strips of the welding tongs. Specifically, the strips are heated by successive waves following one after another in an offset and alternating manner, so that, at each instant, only one heating strip is supplied with power. Thus, the overall energy sent into the heating strips is relatively constant and of low level. Application to welding tongs for welding plastic bags used for handling contaminated materials in gloveboxes.