The invention relates to a method for the manufacture of tubes bent in a U-shape (hairpin tubes) from a nonferrous metal, immediately following a tube production line. For that purpose, according to the invention, the method for the manufacture of tubes bent in a U-shape from a nonferrous metal, immediately following a tube production line, has the consecutive steps of: a) uncoiling the drawn tube material from a basket winder, b) straightening the drawn tube material, c) annealing and subsequently cooling the drawn tube material before or after cutting, for separation into tube portions, to the starting length for a tube bent in a U-shape, and d) bending the tube portions into a U-shape.