A reactor which comprises: at least one pair of auxiliary winding elements (2-1, 2-2) each having a plurality of coil segments (5-1, 5-2) spaced a distance from each other in a direction of the winding axis, wherein the auxiliary winding elements are the same as each other and wherein the auxiliary winding elements are bobbinless; each of the coil segments being wound with a winding wire in a multilayered and aligned winding fashion; wherein the coil segments of the first auxiliary winding element and the coil segments of the second auxiliary winding element are wound in respective directions reverse to each other, the coil segments of the first auxiliary winding element being accommodated within respective space areas (6-1, 6-2), which are delimited respectively between the coil segments of the second auxiliary winding element and an outside in the direction of the winding axis of those coil segments of the second auxiliary winding elements, whereas the coil segments of the second auxiliary winding elements are accommodated within said respective space areas (6-1, 6-2), which are delimited respectively between an outside in the direction of the winding axis of the coil segments of the first auxiliary winding element and the coil segments of the first auxiliary winding element, the coil segments of each of those first and second auxiliary winding elements being so combined as to be adjacently alternately positioned in the direction of the winding axis in a line; and the first and second auxiliary winding elements being connected in parallel to form a main winding body having a hollow defined therein; and a core made of a magnetic material and inserted into the hollow of the main winding body. at least one pair of auxiliary winding elements (2-1, 2-2) each having a plurality of coil segments (5-1, 5-2) spaced a distance from each other in a direction of the winding axis, wherein the auxiliary winding elements are the same as each other and wherein the auxiliary winding elements are bobbinless; each of the coil segments being wound with a winding wire in a multilayered and aligned winding fashion; wherein the coil segments of the first auxiliary winding element and the coil segments of the second auxiliary winding element are wound in respective directions reverse to each other, the coil segments of the first auxiliary winding element being accommodated within respective space areas (6-1, 6-2), which are delimited respectively between the coil segments of the second auxiliary winding element and an outside in the direction of the winding axis of those coil segments of the second auxiliary winding elements, whereas the coil segments of the second auxiliary winding elements are accommodated within said respective space areas (6-1, 6-2), which are delimited respectively between an outside in the direction of the winding axis of the coil segments of the first auxiliary winding element and the coil segments of the first auxiliary winding element, the coil segments of each of those first and second auxiliary winding elements being so combined as to be adjacently alternately positioned in the direction of the winding axis in a line; and the first and second auxiliary winding elements being connected in parallel to form a main winding body having a hollow defined therein; and a core made of a magnetic material and inserted into the hollow of the main winding body.