Limits of Hodge structures in several variables

We define the notion of a morphism of generalized semi-stable type, which is a generalization of the notion of a semistable degeneration over a curve. We partially generalize Steenbrink's results on the limit of Hedge structures to the case of such a morphism, As an application we prove the E-1-degeneration of the relative Hedge-De Rham spectral sequence for this case.