The invention relates to a method for additively manufacturing at least one component region of a component, in particular of a turbine or compressor component, said method comprising at least the following steps: applying a layer of powder (10a-c) to a component platform in the region of a building and joining area; locally melting and/or sintering the powder layer (10a-c), wherein, in the region of the building and joining area, at least one high-energy beam is moved in relation to the component platform, selectively impinging the powder layer (10a-c), at least part of which at least one high-energy beam and the component platform are moved in relation to one another, in the form of a parallel arrangement (16) arranged along a linear feed direction (12); lowering the component platform by a predetermined layer thickness in a lowering direction; and repeating the above-mentioned steps until the component region is completed. According to the invention, the at least one high-energy beam and the component platform are moved in relation to one another for at least two different powder layers (10a-c) in such a way that, in powder layer regions arranged above one another in a lowering direction, each parallel arrangement (16) of each powder layer (10a-c) is arranged at different angles to each linear feed direction (12). The invention also relates to a device for carrying out a method of this type.