  We introduce and study a new class of representations of surface groups into
Lie groups of Hermitian type, called {\em weakly maximal} representations. We
prove that weakly maximal representations are discrete and injective and we
describe the structure of the Zariski closure of their image. Furthermore we
prove that the set of weakly maximal representations is a closed subset of the
representation variety and describe its relation to other geometrically
significant subsets of the representation variety.
