  Generalized Calabi-Yau structures, a notion recently introduced by Hitchin,
are studied in the case of K3 surfaces. We show how they are related to the
classical theory of K3 surfaces and to moduli spaces of certain SCFT as studied
by Aspinwall and Morrison. It turns out that K3 surfaces and symplectic
structures are both special cases of this general notion. The moduli space of
generalized Calabi-Yau structures admits a canonical symplectic form with
respect to which the moduli space of symplectic structures is Lagrangian. The
standard theory of K3 surfaces implies surjectivity of the period map and a
weak form of the Global Torelli theorem.
