Superembeddings, nonlinear supersymmetry and five-branes

We examine general properties of superembeddings, i.e. embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of nonlinearly realized supersymmetry is clarified, and we demonstrate how the latter arises as a special case of the former. As an illustration, the super-5-brane in seven dimensions, containing a self-dual three-form world volume field strength, is formulated in both languages, and provides an example of a model where the embedding condition does not suffice to put the theory on-shell.