The present invention relates to methods and apparatus for winding a plurality of strands (20) into a multilayered package (54). The preferred method includes: a) supplying a plurality of strands (20); b) aligning each of the strands in generally adjacent and coplanar alignment (16); c) oscillating the strands about a pivot axis while maintaining the strands in alignment (22); d) reciprocating a reciprocating device generally parallel to a central axis of rotation of a rotatable packaging collector (54); and e) winding the strands about an arcuate surface (57) of the collector to form a multilayered package, such that within each layer of strands wound upon the surface of the rotatable packaging collector (54), each of the plurality of strands is adjacent to each other and essentially free of overlap. The preferred apparatus includes a strand supply device (12); an alignment device (18); a strand oscillating device (22) including a strand guide (24) adapted to oscillate about a pivot axis and having a first arm and a second arm spaced apart to receive and align the strands; a winding device including a rotatable packaging collector (54) having an arcuate surface (57) adapted to receive the strands to form a multilayered package; and a reciprocating device, such that within each layer of strands wound upon the surface of the rotatable packaging collector (54), each of the plurality of strands is adjacent to each other and essentially free of overlap.