Mesh welding machine operating continuously according to the electrical resistance principle, comprising a stationary outer longitudinal frame, on which, in a manner resting thereon, a horizontal set of parallel longitudinal wires can be moved continuously in a production direction by means of a feeding device, and comprising a removal apparatus, by means of which cross wires can be removed from a coil or rings and fed to a transfer device extending transversely to the set of longitudinal wires, in which transfer device a plurality of cross wires can be received and, from there, can be conveyed one after another in turn towards the longitudinal wires and brought into contact with said longitudinal wires in a correct orientation according to the pitch of the cross wires and can be set down there, and comprising electrodes and counter electrodes, the weld surfaces of which can be pressed against one another so as to have points of intersection therebetween, which points of intersection are formed between the longitudinal wires and the cross wires, both the upper electrodes and the lower counter electrodes being arranged on an inner frame which is mounted on the stationary frame and is movable back and forth periodically in the longitudinal direction relative to said stationary frame, and the upper electrodes being mounted on the movable frame so as to be able to move from an upper position downwards onto the points of intersection that rest on the lower counter electrodes, said upper electrodes reaching a lower first position of the start of the welding process so as to be in contact with the points of intersection and then, by moving the frame in the longitudinal direction together with the lower counter electrodes while maintaining contact pressure, traveling synchronously with the mesh into a second position of the end of the welding process, which second position is at the same height level and located downstream with respect to a direction of flow, and then, by moving the inner frame back, the electrodes and the counter electrodes returning to their earlier positions with respect to the longitudinal direction, while the upper electrodes can be moved first vertically upwards again and then downwards into the earlier, lower first position of the start of the welding process on the following cross wire(s), it being possible to bring the cross wires into contact with the set of longitudinal wires in the correct orientation by means of gripping fingers, characterised in that the gripping fingers provided for each of the weld points can travel to the transfer device which is intended for receiving the cross wires and receives a plurality of cross wires arriving from the removal apparatus, and said fingers then can be moved together with a received cross wire towards the points of intersection until the cross wire contacts the points of intersection at a time immediately before the upper electrodes, and the gripping fingers then travel, by means of the movable frame, first alone along a first section before welding begins and then together with the electrodes and the counter electrodes along another section of the horizontal path travelled by said electrodes synchronously with the longitudinal wires of the mesh to be formed, whereupon the synchronous travel of the electrodes and the counter electrodes can be continued until welding is completed.