The method and the apparatus of the invention serve to shift at least some sheets of successive stacks of overlapping sheets so that the originally straight holes which are provided along one marginal portion of each stack are converted into arcuate passages adapted to more readily receive the convolutions of spirals serving to pivotably couple the sheets of the stacks to each other. This is accomplished by inserting into one or both ends of some or all of the holes a discrete pin-shaped displacing member which is thereupon pivoted to thus shift at least some of the sheets relative to the neighboring sheets. In order to speed up the shifting of sheets, the displacing member or members is or are pivoted during withdrawal from the respective hole or holes to move its or their tips along arcuate paths at least approximating the curvatures of the convolutions which are to be introduced into the thus converted holes.