The method according to the invention is used to produce a coil winding (70) which can be inserted into the grooves of a stator or rotor of an electric machine. While using a winding template (26) and a wire handling device (14), the invention proposes carrying out a displacement process between a first and a second holding region (34, 36) even before the wires (32) are initially wound onto the winding template (26) in order to produce an inclined wire section (40) which is subsequently shaped into winding heads (42) by means of a rotating/winding process. The novel method offers the advantage that all of the wires (32) of a coil winding (70) can be processed simultaneously using a comparably simple winding device (110). The projection of the winding heads (42) over the stator can also be minimized.