abstract: A generalized deformation of a complex manifold is defined algebraically as a solution, up to gauge, of the Maurer-Cartan equation in the algebra of polyvector fields. We show that in the Kaehler case, every generalized deformation gives a canonical sequence of holomorphic maps into the Grassmannian of graded subspaces of the De Rham cohomology. For classical deformations the above maps reduces to Griffiths period maps.