Continuous strip materials supplied in rolls are spliced automatically at the moment of use by a series of steps in which the leading end of the strip decoiled from a new roll is arranged first on the locating and striking face of a suction bar capable of movement between an at-rest position and a splicing position, whereupon the trailing end of the depleted strip decoiling from the roll still in use is restrained against a fixed reference surface coinciding with the splicing position, a transverse cut made through the trailing end of the depleted strip, and the leading end of the new strip brought into contact with the area of the trailing end of the depleted strip terminating in the cut, and the joined ends are then secured by heat-sealing or by applying an adhesive or a double-sided sticker.