  In this paper we will introduce a new notion of geometric structures defined
by systems of closed differential forms in term of the Clifford algebra of the
direct sum of the tangent bundle and the cotangent bundle on a manifold. We
develop a unified approach of a deformation problem and establish a criterion
of unobstructed deformations of the structures from a cohomological point of
view. We construct the moduli spaces of the structures by using the action of
b-fields and show that the period map of the moduli space is locally injective
under a cohomological condition (the local Torelli type theorem). We apply our
approach to generalized Calabi-Yau (metrical) structures and obtain an analog
of the theorem by Bogomolov-Tian-Todorov. Further we prove that deformations of
generalized Spin(7) structures are unobstructed.
