The invention relates to apparatus for and a method of moving a grid (G) longitudinally in stepwise fashion through a multi-spot welding machine by means of an element (5) arranged to engage a transverse rod (D) of the grid at a starting position, move the grid (G) forward through a number of steps at a first mean speed, and thereafter disengage from the rod (D) and return to the starting position at a mean speed greater than the first mean speed. The movement of the element (5) is controlled by a computer (31) so as to return to its starting position if the time required for its return from the position which it would occupy after the next step is greater than a preset maximum standstill time between steps.