A resistance seam welding machine is described, particularly for the longitudinal seam welding of can bodies, wherein, in the secondary loop (16), feed and return lines are constructed partially as a double line (18, 28) and in all the remaining portion (18a, 18b, 18c, 20, 24, 26) in the form of a substantially coaxial line. The voltage loss occurring in the secondary loop (16) between welding transformer (14) and welding position (8, 10) and the heat due to energy losses in the machine parts adjacent to the secondary loop are considerably reduced as a result of this construction of the feed return lines.