Profiles (50) are formed in a production line with a cross-section that varies along their length from a plane metal strip (10) that is unwound from a tape reel (9). Edge cutters (14) and roll-forming units (17-24) are displaceable individually sideways relative to the strip, and are individually controlled. The formed profile is curved in a curving station integrated into the production line and having roller pairs (82, 84; 83, 85) that can be controlled to roll sides of the profile (50) such that they become thinner so that the profile is curved or twisted as it is formed. The roller pairs and the sideways displacement and the angular motion of the roll-forming units are controlled so that the roller pairs follow the sides and such that a line (II) between the axles of one roller pair is held perpendicular to the surface being rolled.