A cable winding machine for winding together a multiple number of subconductors into a composite cable includes holding means for holding a first subconductor in the machine direction, and in a predetermined orientation of the first subconductor about its longitudinal axis as it moves through the machine; a first rotating member arranged and rotate the second subconductor around the first subconductor as the second subconductor moves through the machine and one or more further rotating members arranged to hold further subconductors aligned in the machine direction and in a predetermined orientation about their longitudinal axes and rotate the further subconductors around the subconductors wound with one another in the first winding stage of the machine.