A method uses a powder bed-based additive production of components such as laser melting. The interior wall of a hollow cylinder is used as a construction platform. Progressive production of the component is possible by rotating the hollow cylinder step-by-step in direction. This allows production of components without set-up times as the components can emerge from the powder bed as rotation continues and can be separated from the hollow cylinder by a separating device. The space requirement for the hollow cylinder in this arrangement is relatively small.