A device and a method for producing a batch of products having a multiplicity of interfolded, generally rectangular sheets including wet wipes, from a limited amount of a web material, at a high production speed and in efficiently used floor space. The method includes the steps of folding a first and second ribbons by a first and second folding devices, respectively; interfolding the ribbons to provide a first pair of ribbons; securing the first pair to a perimeter surface of a cyclical accumulator; accumulating the first pair onto the perimeter surface by providing a tangential velocity to the first pair; interfolding the first pair with a newly formed second pair of ribbons; rotating the perimeter surface of the cyclical accumulator to provide the tangential velocity to the second pair so as to superimpose the second pair onto the first pair of ribbons; displacing the cyclical accumulator linearly to accommodate the second pair in a machine direction; repeating the steps of rotating and linearly displacing the cyclical accumulator to form successive pairs of ribbons until a desired stack of ribbons is accumulated on the perimeter surface; and selectively cutting through the stack of ribbons.