Classification hierarchies are trees where links codify the fact that a node lower in the hierarchy contains documents whose contents are more specific than those one level above. In turn, multiple classification hierarchies can be connected by semantic links which represent mappings among them and which can be computed, e.g., by ontology matching. In this paper we describe how these two types of links can be used to define a semantic overlay network which can cover any number of peers and which can be flooded to perform semantic search on documents, i.e., to perform semantic flooding. We have evaluated our approach in a simulation of the network of 10,000 peers containing classifications which are fragments of the DMoz Web directory. The results are very promising and show that, in our approach, only a relatively small number of peers needs to be queried in order to achieve high accuracy.