In a process for winding a continuously supplied band (5) onto a bobbin (2), with the bobbin (2) being rotated and the band (5) being reciprocated along the entire length of the bobbin (2) at a winding angle (α) by means of a cross-winding device (4), each time the bobbin diameter has increased by a particular value, the winding ratio, i.e., the ratio between the number of bobbin rotations and the reciprocating motion (to-and-fro stroke) of the cross-winding device is stepwisely changed such that the winding ratio will change in essentially integral steps.