A continuous web of cigarette paper or other wrapping material, particularly for smokers' products, is split by a pair of rotary knives into two strips which are fed to discrete strip processing units, such as wrapping units for rod-like tobacco fillers. If the width of the web and/or of one strip or both strips departs from a predetermined width, the web is shifted sideways and/or at least one of the strips is moved relative to the other strip to at least partially compensate for departures of monitored width from the predetermined width. This can be accomplished by changing the orientation of a frame for rollers which flank the web and/or by changing the level or levels of one or more rolls which advance the web by way of the strips.