Method and assembly for a continuous or semi-continuous additive manufacture of components

In a photochemical method for the additive manufacture of components (7), a construction material is used that can undergo an additional phase transition, which can be controlled by cooling, between a liquid phase and a solid aggregate state as a second solid phase during the additive manufacture, said additional phase transition not influencing the first solid phase produced by radiation for constructing the components. The additional phase transition is controlled during the construction of the components (7) such that component regions solidified while forming the first phase are supported by surrounding construction material in the second solid phase. In the method, a block (9) of solidified construction material produced by the transition into the second solid phase is conveyed opposite the construction direction by an advancing device (3) which laterally approaches and engages the block (9) in order to construct the components (7), thus allowing a continuous manufacture of components without interruptions resulting from changing the construction platform.